{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.dates as mdates\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "from sympy import Symbol, symbols, Matrix, sin, cos\n",
    "from sympy import init_printing\n",
    "init_printing(use_latex=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Extended Kalman Filter Implementation for Constant Turn Rate and Velocity (CTRV) Vehicle Model in Python\n",
    "\n",
    "![Extended Kalman Filter Step](Extended-Kalman-Filter-Step.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "[Wikipedia](http://en.wikipedia.org/wiki/Extended_Kalman_filter) writes: In the extended Kalman filter, the state transition and observation models need not be linear functions of the state but may instead be differentiable functions.\n",
    "\n",
    "$\\boldsymbol{x}_{k} = g(\\boldsymbol{x}_{k-1}, \\boldsymbol{u}_{k-1}) + \\boldsymbol{w}_{k-1}$\n",
    "\n",
    "$\\boldsymbol{z}_{k} = h(\\boldsymbol{x}_{k}) + \\boldsymbol{v}_{k}$\n",
    "\n",
    "Where $w_k$ and $v_k$ are the process and observation noises which are both assumed to be zero mean Multivariate Gaussian noises with covariance matrix $Q$ and $R$ respectively.\n",
    "\n",
    "The function $g$ can be used to compute the predicted state from the previous estimate and similarly the function $h$ can be used to compute the predicted measurement from the predicted state. However, $g$ and $h$ cannot be applied to the covariance directly. Instead a matrix of partial derivatives (the Jacobian matrix) is computed.\n",
    "\n",
    "At each time step, the Jacobian is evaluated with current predicted states. These matrices can be used in the Kalman filter equations. This process essentially linearizes the non-linear function around the current estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## State Vector - Constant Turn Rate and Velocity Vehicle Model (CTRV)\n",
    "\n",
    "Situation covered: You have a velocity sensor, which measures the vehicle speed ($v$) in heading direction ($\\psi$) and a yaw rate sensor ($\\dot \\psi$) which both have to fused with the position ($x$ & $y$) from a GPS sensor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Constant Turn Rate, Constant Velocity Model for a vehicle ![CTRV Model](CTRV-Model.png)\n",
    "\n",
    "$$x_k= \\left[ \\matrix{ x \\\\ y \\\\ \\psi \\\\ v \\\\ \\dot\\psi} \\right] = \\left[ \\matrix{ \\text{Position X} \\\\ \\text{Position Y} \\\\ \\text{Heading} \\\\ \\text{Velocity} \\\\ \\text{Yaw Rate}} \\right]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "numstates=5 # States"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We have different frequency of sensor readings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "dt = 1.0/50.0 # Sample Rate of the Measurements is 50Hz\n",
    "dtGPS=1.0/10.0 # Sample Rate of GPS is 10Hz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Developing the math behind dynamic model\n",
    "\n",
    "All symbolic calculations are made with [Sympy](http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-5-Sympy.ipynb). Thanks!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "vs, psis, dpsis, dts, xs, ys, lats, lons = symbols('v \\psi \\dot\\psi T x y lat lon')\n",
    "\n",
    "gs = Matrix([[xs+(vs/dpsis)*(sin(psis+dpsis*dts)-sin(psis))],\n",
    "             [ys+(vs/dpsis)*(-cos(psis+dpsis*dts)+cos(psis))],\n",
    "             [psis+dpsis*dts],\n",
    "             [vs],\n",
    "             [dpsis]])\n",
    "state = Matrix([xs,ys,psis,vs,dpsis])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Dynamic Function $g$\n",
    "\n",
    "This formulas calculate how the state is evolving from one to the next time step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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wEqp/dVp/27PlCt3yW0M219QHDC5/T4G38Qj75p8uwDfB79I0XRR/oSx2p9n+5Y1QDJo4\n9QNlsQmc8kEcKObxKbt6oFiGU17rQDGPT9nVA8UynPJaB4p5fMquHiiW4ZTXOlDM41N29UdQbPwb\nEj+CYtuTtD8xAiyrVX+p9Stl8S8xWvf9MygeM2Prmbmu0fTU2M+UxQPF9ZK2qtHAxyEyMf5KWWzg\n4xD/AhSbrtDt9xfb+TjEL5fFdj4O8cMoNvRxiB9GUfwvr0x6/uZS+89o4b+8/gaqjNf2UWzm4xA/\njWLqIxKZRH39UvtlsZmPQ2Typn0Um/k4xG+jmPiIRCZRX7/0A2UR/j08+tOzr+OUd/gTKLY9iAaA\nfwLFptnIWEo1iuo/jP2/SuaL73GVInDV//+M7xiojfyJJVU7jrMI3DV43f8BeMqDegRNMWAAAAAA\nSUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}x + \\frac{v}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\y + \\frac{v}{\\dot\\psi} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\T \\dot\\psi + \\psi\\\\v\\\\\\dot\\psi\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡    v⋅(-sin(\\psi) + sin(T⋅\\dot\\psi + \\psi))⎤\n",
       "⎢x + ───────────────────────────────────────⎥\n",
       "⎢                    \\dot\\psi               ⎥\n",
       "⎢                                           ⎥\n",
       "⎢    v⋅(cos(\\psi) - cos(T⋅\\dot\\psi + \\psi)) ⎥\n",
       "⎢y + ────────────────────────────────────── ⎥\n",
       "⎢                   \\dot\\psi                ⎥\n",
       "⎢                                           ⎥\n",
       "⎢             T⋅\\dot\\psi + \\psi             ⎥\n",
       "⎢                                           ⎥\n",
       "⎢                     v                     ⎥\n",
       "⎢                                           ⎥\n",
       "⎣                 \\dot\\psi                  ⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Calculate the Jacobian of the Dynamic function $g$ with respect to the state vector $x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAB4AAAB9CAMAAACCjiNkAAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}x\\\\y\\\\\\psi\\\\v\\\\\\dot\\psi\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡   x    ⎤\n",
       "⎢        ⎥\n",
       "⎢   y    ⎥\n",
       "⎢        ⎥\n",
       "⎢  \\psi  ⎥\n",
       "⎢        ⎥\n",
       "⎢   v    ⎥\n",
       "⎢        ⎥\n",
       "⎣\\dot\\psi⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3hk4CXZwZkhZbc2SGQCxKIgYUu58Z9/vnnb4/A8rkC61G6ScEeBFhH47DuZZ+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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0 & \\frac{v}{\\dot\\psi} \\left(- \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{1}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T v}{\\dot\\psi} \\cos{\\left (T \\dot\\psi + \\psi \\right )} - \\frac{v}{\\dot\\psi^{2}} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\0 & 1 & \\frac{v}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{1}{\\dot\\psi} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T v}{\\dot\\psi} \\sin{\\left (T \\dot\\psi + \\psi \\right )} - \\frac{v}{\\dot\\psi^{2}} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\0 & 0 & 1 & 0 & T\\\\0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡      v⋅(-cos(\\psi) + cos(T⋅\\dot\\psi + \\psi))  -sin(\\psi) + sin(T⋅\\dot\\psi + \n",
       "⎢1  0  ───────────────────────────────────────  ──────────────────────────────\n",
       "⎢                      \\dot\\psi                               \\dot\\psi        \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢      v⋅(-sin(\\psi) + sin(T⋅\\dot\\psi + \\psi))  cos(\\psi) - cos(T⋅\\dot\\psi + \\\n",
       "⎢0  1  ───────────────────────────────────────  ──────────────────────────────\n",
       "⎢                      \\dot\\psi                              \\dot\\psi         \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢0  0                     1                                      0            \n",
       "⎢                                                                             \n",
       "⎢0  0                     0                                      1            \n",
       "⎢                                                                             \n",
       "⎣0  0                     0                                      0            \n",
       "\n",
       "\\psi)  T⋅v⋅cos(T⋅\\dot\\psi + \\psi)   v⋅(-sin(\\psi) + sin(T⋅\\dot\\psi + \\psi))⎤\n",
       "─────  ────────────────────────── - ───────────────────────────────────────⎥\n",
       "                \\dot\\psi                                   2               ⎥\n",
       "                                                   \\dot\\psi                ⎥\n",
       "                                                                           ⎥\n",
       "psi)   T⋅v⋅sin(T⋅\\dot\\psi + \\psi)   v⋅(cos(\\psi) - cos(T⋅\\dot\\psi + \\psi)) ⎥\n",
       "────   ────────────────────────── - ────────────────────────────────────── ⎥\n",
       "                \\dot\\psi                                  2                ⎥\n",
       "                                                  \\dot\\psi                 ⎥\n",
       "                                                                           ⎥\n",
       "                                        T                                  ⎥\n",
       "                                                                           ⎥\n",
       "                                        0                                  ⎥\n",
       "                                                                           ⎥\n",
       "                                        1                                  ⎦"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gs.jacobian(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "It has to be computed on every filter step because it consists of state variables!\n",
    "\n",
    "To Sympy Team: A `.to_python` and `.to_c` and `.to_matlab` whould be nice to generate code, like it already works with `print latex()`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Initial Uncertainty $P_0$\n",
    "\n",
    "Initialized with $0$ means you are pretty sure where the vehicle starts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 1000.,     0.,     0.,     0.,     0.],\n",
      "       [    0.,  1000.,     0.,     0.,     0.],\n",
      "       [    0.,     0.,  1000.,     0.,     0.],\n",
      "       [    0.,     0.,     0.,  1000.,     0.],\n",
      "       [    0.,     0.,     0.,     0.,  1000.]]), (5, 5))\n"
     ]
    }
   ],
   "source": [
    "P = np.diag([1000.0, 1000.0, 1000.0, 1000.0, 1000.0])\n",
    "print(P, P.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11677c550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5, 5))\n",
    "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Initial Covariance Matrix $P$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,4.5])\n",
    "plt.ylim([4.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Process Noise Covariance Matrix $Q$\n",
    "\n",
    "\"*The state uncertainty model models the disturbances which excite the linear system. Conceptually, it estimates how bad things can get when the system is run open loop for a given period of time.*\" - Kelly, A. (1994). A 3D state space formulation of a navigation Kalman filter for autonomous vehicles, (May). Retrieved from http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA282853"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[  3.09760000e-06,   0.00000000e+00,   0.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   3.09760000e-06,   0.00000000e+00,\n",
      "          0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   4.00000000e-06,\n",
      "          0.00000000e+00,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "          3.09760000e-02,   0.00000000e+00],\n",
      "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "          0.00000000e+00,   4.00000000e-04]]), (5, 5))\n"
     ]
    }
   ],
   "source": [
    "sGPS     = 0.5*8.8*dt**2  # assume 8.8m/s2 as maximum acceleration, forcing the vehicle\n",
    "sCourse  = 0.1*dt # assume 0.1rad/s as maximum turn rate for the vehicle\n",
    "sVelocity= 8.8*dt # assume 8.8m/s2 as maximum acceleration, forcing the vehicle\n",
    "sYaw     = 1.0*dt # assume 1.0rad/s2 as the maximum turn rate acceleration for the vehicle\n",
    "\n",
    "Q = np.diag([sGPS**2, sGPS**2, sCourse**2, sVelocity**2, sYaw**2])\n",
    "print(Q, Q.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iICIGxo8f3+THm9lI5BBOImI98BgwQdLbJO0CLAIEfCYiXupAjWY2wvVzCLdynPBdwDSy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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11673a450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5, 5))\n",
    "im = plt.imshow(Q, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Process Noise Covariance Matrix $Q$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(8))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(7),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(8))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(7),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,4.5])\n",
    "plt.ylim([4.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Real Measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Read '2014-03-26-000-Data.csv' successfully.\n"
     ]
    }
   ],
   "source": [
    "#path = './../RaspberryPi-CarPC/TinkerDataLogger/DataLogs/2014/'\n",
    "datafile = '2014-03-26-000-Data.csv'\n",
    "\n",
    "date, \\\n",
    "time, \\\n",
    "millis, \\\n",
    "ax, \\\n",
    "ay, \\\n",
    "az, \\\n",
    "rollrate, \\\n",
    "pitchrate, \\\n",
    "yawrate, \\\n",
    "roll, \\\n",
    "pitch, \\\n",
    "yaw, \\\n",
    "speed, \\\n",
    "course, \\\n",
    "latitude, \\\n",
    "longitude, \\\n",
    "altitude, \\\n",
    "pdop, \\\n",
    "hdop, \\\n",
    "vdop, \\\n",
    "epe, \\\n",
    "fix, \\\n",
    "satellites_view, \\\n",
    "satellites_used, \\\n",
    "temp = np.loadtxt(datafile, delimiter=',', unpack=True, \n",
    "                  converters={1: mdates.strpdate2num('%H%M%S%f'),\n",
    "                              0: mdates.strpdate2num('%y%m%d')},\n",
    "                  skiprows=1)\n",
    "\n",
    "print('Read \\'%s\\' successfully.' % datafile)\n",
    "\n",
    "# A course of 0° means the Car is traveling north bound\n",
    "# and 90° means it is traveling east bound.\n",
    "# In the Calculation following, East is Zero and North is 90°\n",
    "# We need an offset.\n",
    "course =(-course+90.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Measurement Function $h$\n",
    "\n",
    "Matrix $J_H$ is the Jacobian of the Measurement function $h$ with respect to the state. Function $h$ can be used to compute the predicted measurement from the predicted state.\n",
    "\n",
    "If a GPS measurement is available, the following function maps the state to the measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAB4AAABkCAMAAACmV3A3AAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\nAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}x\\\\y\\\\v\\\\\\dot\\psi\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡   x    ⎤\n",
       "⎢        ⎥\n",
       "⎢   y    ⎥\n",
       "⎢        ⎥\n",
       "⎢   v    ⎥\n",
       "⎢        ⎥\n",
       "⎣\\dot\\psi⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hs = Matrix([[xs],\n",
    "             [ys],\n",
    "             [vs],\n",
    "             [dpsis]])\n",
    "hs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJcAAABkCAMAAAC8R1L8AAAAP1BMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADFBd4eAAAAFHRS\nTlMAMquZdlQQQO0wRO/NZondIrt8bFiOv0QAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAOSSURBVGgF\n7ZvbdtowFEQFGJNyJ/X/f2stmyQaCZ29TimEdImXgMcjb48Uw8QhLIbpsQyv8TjNOCEshlU3Ptav\ngRUOEWY5RK7FiyB9YRw8XP3qeDga5wC6R8651rv+Czp/th+nuj+d882fr0H3yMLVL1fLoc512EWC\n4/6TI3sCuksWrvE4ncF1mX5j19U9QHfJHq5h4toOtV9c0F2yg6sfVnHitkOXzd/1Jeg+2cF1Ho6R\nYDH/KNlA98kurikvg8vUz3PcNXsmO7hgIgLoPtnBFeaFu4Z1X9XBrrKH63KJi+pQv07YOthV9nDN\nF8YVXFerOthV9nCFU3wf2tXfIEH3yMq1Wu6G/fJQXgPmLf1x/ABSxwqge2TlqgE9f3vj8mXe8mp5\n+RLw7d3WV8vLl4Bvb11f0DxpaLB7ZOWC5hmCWXsD2D2ycEHzhNobwO6ShQua5ziNVu0NYHfJwgXN\nk7jA7pJTLmgscdVbeYHdJ6dc0DyJC+w+WbnMYspcpj0rrnG09JHJKRckHUd56jxuhs1MrtUyPZuP\n5xYX9V4YXeX39O+YWi0/WNKfJhfYXXI6j9cLY7WYjoAmlzbT9HSm5y5ZuLC42lxk//teC80Tam/r\ntcUaedoGXV9POyweqHFhRLJDy0viwBcxr76r3xPCAR60w3m8efHj7z8+KJtbw/6Mde9pnjfOEuw3\nHOkmcWtenuaZDnl9DnaoxeIWLlfzLLnADrVY3cLlap4lF9hHg/WxUt3C5WqeJRfYgUvdKRf0IZDp\nPl88DyOvbPSUy9c8i7zADlyZW7nuKaYha6YFt51X5k65sijzgUH+9/O4efs1M2i1zLmot6Jurq/M\n/fsted92Nc8CO4B9NBjrPnOn80i9Foop2YFLRxeuO4sp2e281K1c0GtBpl4LtVhGV65yzXzXlsbl\nS77l1fLyJeDbu62vlpcvAd/eur6kWpYDgRxAB1mOp1xSLWW/6QXId96vldorXFotCy6Q77xfq7VX\nuLRaFlwg33m/djxc8nFWuLRaFlwgXz+hV/9PmexVLig8IFMfIns9r6xa5nmBPPZH8/+UQY5Hq8xj\nVi1LLrP2Uq+F0Q0uSBrkx81jVi3zvEgmHVpzfR6zallwUW8FHWSDS6tlwQUy9VqyV9d90GpZcJFM\nOtyvNbikWpZcIFOvBbvUXrnelyTftqVx+aJvef1Peb3m90X7+AXNrtv6kn7Y3tP3Rbsu/AEd1E6s\ny97VvAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0 & 0 & 0 & 0\\\\0 & 1 & 0 & 0 & 0\\\\0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  0  0  0  0⎤\n",
       "⎢             ⎥\n",
       "⎢0  1  0  0  0⎥\n",
       "⎢             ⎥\n",
       "⎢0  0  0  1  0⎥\n",
       "⎢             ⎥\n",
       "⎣0  0  0  0  1⎦"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JHs=hs.jacobian(state)\n",
    "JHs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "If no GPS measurement is available, simply set the corresponding values in $J_h$ to zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Measurement Noise Covariance $R$\n",
    "\n",
    "\"In practical use, the uncertainty estimates take on the significance of relative weights of state estimates and measurements. So it is not so much important that uncertainty is absolutely correct as it is that it be relatively consistent across all models\" - Kelly, A. (1994). A 3D state space formulation of a navigation Kalman filter for autonomous vehicles, (May). Retrieved from http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA282853"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[  3.60000000e+01,   0.00000000e+00,   0.00000000e+00,\n",
      "           0.00000000e+00],\n",
      "        [  0.00000000e+00,   3.60000000e+01,   0.00000000e+00,\n",
      "           0.00000000e+00],\n",
      "        [  0.00000000e+00,   0.00000000e+00,   1.00000000e+00,\n",
      "           0.00000000e+00],\n",
      "        [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
      "           1.00000000e-02]]), (4, 4))\n"
     ]
    }
   ],
   "source": [
    "varGPS = 6.0 # Standard Deviation of GPS Measurement\n",
    "varspeed = 1.0 # Variance of the speed measurement\n",
    "varyaw = 0.1 # Variance of the yawrate measurement\n",
    "R = np.matrix([[varGPS**2, 0.0, 0.0, 0.0],\n",
    "               [0.0, varGPS**2, 0.0, 0.0],\n",
    "               [0.0, 0.0, varspeed**2, 0.0],\n",
    "               [0.0, 0.0, 0.0, varyaw**2]])\n",
    "\n",
    "print(R, R.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vI+LFCm0sjoh5ETFv1qxZtYo2s3bIoacGxSroWyhWQbcEdqC4qNvVTRZmZu039D21pLMK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\nONTMLCsONTPLikPNzLLy/wHTv/eW2aj4dgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11676ef90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(4.5, 4.5))\n",
    "im = plt.imshow(R, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Measurement Noise Covariance Matrix $R$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(5))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(4),('$x$', '$y$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(5))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(4),('$x$', '$y$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,3.5])\n",
    "plt.ylim([3.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Identity Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 1.,  0.,  0.,  0.,  0.],\n",
      "       [ 0.,  1.,  0.,  0.,  0.],\n",
      "       [ 0.,  0.,  1.,  0.,  0.],\n",
      "       [ 0.,  0.,  0.,  1.,  0.],\n",
      "       [ 0.,  0.,  0.,  0.,  1.]]), (5, 5))\n"
     ]
    }
   ],
   "source": [
    "I = np.eye(numstates)\n",
    "print(I, I.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## Approx. Lat/Lon to Meters to check Location"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "RadiusEarth = 6378388.0 # m\n",
    "arc= 2.0*np.pi*(RadiusEarth+altitude)/360.0 # m/°\n",
    "\n",
    "dx = arc * np.cos(latitude*np.pi/180.0) * np.hstack((0.0, np.diff(longitude))) # in m\n",
    "dy = arc * np.hstack((0.0, np.diff(latitude))) # in m\n",
    "\n",
    "mx = np.cumsum(dx)\n",
    "my = np.cumsum(dy)\n",
    "\n",
    "ds = np.sqrt(dx**2+dy**2)\n",
    "\n",
    "GPS=(ds!=0.0).astype('bool') # GPS Trigger for Kalman Filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Initial State"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 0.        ],\n",
      "        [ 0.        ],\n",
      "        [-4.08756111],\n",
      "        [ 0.67322222],\n",
      "        [-0.32660346]]), (5, 1))\n"
     ]
    },
    {
     "data": {
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      "text/latex": [
       "$$\\left ( -0.00180704898447, \\quad 0.00180704898447, \\quad -0.00278237674761, \\quad 0.00278237674761\\right )$$"
      ],
      "text/plain": [
       "(-0.00180704898447, 0.00180704898447, -0.00278237674761, 0.00278237674761)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NLAxJUhMLQ5LUxMKQJDWxMCRJTSwMSVITC0OS1MTCkCQ1sTAkSU0sDElSEwtDktTEwpAk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\nSWpiYUiSmlgYkqQmFoYkqYmFIUlq8v8AnjojL1r99JQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116795490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.matrix([[mx[0], my[0], course[0]/180.0*np.pi, speed[0]/3.6+0.001, yawrate[0]/180.0*np.pi]]).T\n",
    "print(x, x.shape)\n",
    "\n",
    "U=float(np.cos(x[2])*x[3])\n",
    "V=float(np.sin(x[2])*x[3])\n",
    "\n",
    "plt.quiver(x[0], x[1], U, V)\n",
    "plt.scatter(float(x[0]), float(x[1]), s=100)\n",
    "plt.title('Initial Location')\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Put everything together as a measurement vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4, 10800)\n"
     ]
    }
   ],
   "source": [
    "measurements = np.vstack((mx, my, speed/3.6, yawrate/180.0*np.pi))\n",
    "# Lenth of the measurement\n",
    "m = measurements.shape[1]\n",
    "print(measurements.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# Preallocation for Plotting\n",
    "x0 = []\n",
    "x1 = []\n",
    "x2 = []\n",
    "x3 = []\n",
    "x4 = []\n",
    "x5 = []\n",
    "Zx = []\n",
    "Zy = []\n",
    "Px = []\n",
    "Py = []\n",
    "Pdx= []\n",
    "Pdy= []\n",
    "Pddx=[]\n",
    "Pddy=[]\n",
    "Kx = []\n",
    "Ky = []\n",
    "Kdx= []\n",
    "Kdy= []\n",
    "Kddx=[]\n",
    "dstate=[]\n",
    "\n",
    "\n",
    "def savestates(x, Z, P, K):\n",
    "    x0.append(float(x[0]))\n",
    "    x1.append(float(x[1]))\n",
    "    x2.append(float(x[2]))\n",
    "    x3.append(float(x[3]))\n",
    "    x4.append(float(x[4]))\n",
    "    Zx.append(float(Z[0]))\n",
    "    Zy.append(float(Z[1]))    \n",
    "    Px.append(float(P[0,0]))\n",
    "    Py.append(float(P[1,1]))\n",
    "    Pdx.append(float(P[2,2]))\n",
    "    Pdy.append(float(P[3,3]))\n",
    "    Pddx.append(float(P[4,4]))\n",
    "    Kx.append(float(K[0,0]))\n",
    "    Ky.append(float(K[1,0]))\n",
    "    Kdx.append(float(K[2,0]))\n",
    "    Kdy.append(float(K[3,0]))\n",
    "    Kddx.append(float(K[4,0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Extended Kalman Filter\n",
    "\n",
    "![Extended Kalman Filter Step](Extended-Kalman-Filter-Step.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "$$x_k= \\begin{bmatrix} x \\\\ y \\\\ \\psi \\\\ v \\\\ \\dot\\psi \\end{bmatrix} = \\begin{bmatrix} \\text{Position X} \\\\ \\text{Position Y} \\\\ \\text{Heading} \\\\ \\text{Velocity} \\\\ \\text{Yaw Rate} \\end{bmatrix} =  \\underbrace{\\begin{matrix}x[0] \\\\ x[1] \\\\ x[2] \\\\ x[3] \\\\ x[4]  \\end{matrix}}_{\\textrm{Python Nomenclature}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "for filterstep in range(m):\n",
    "\n",
    "    # Time Update (Prediction)\n",
    "    # ========================\n",
    "    # Project the state ahead\n",
    "    # see \"Dynamic Matrix\"\n",
    "    if np.abs(yawrate[filterstep])<0.0001: # Driving straight\n",
    "        x[0] = x[0] + x[3]*dt * np.cos(x[2])\n",
    "        x[1] = x[1] + x[3]*dt * np.sin(x[2])\n",
    "        x[2] = x[2]\n",
    "        x[3] = x[3]\n",
    "        x[4] = 0.0000001 # avoid numerical issues in Jacobians\n",
    "        dstate.append(0)\n",
    "    else: # otherwise\n",
    "        x[0] = x[0] + (x[3]/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2]))\n",
    "        x[1] = x[1] + (x[3]/x[4]) * (-np.cos(x[4]*dt+x[2])+ np.cos(x[2]))\n",
    "        x[2] = (x[2] + x[4]*dt + np.pi) % (2.0*np.pi) - np.pi\n",
    "        x[3] = x[3]\n",
    "        x[4] = x[4]\n",
    "        dstate.append(1)\n",
    "    \n",
    "    # Calculate the Jacobian of the Dynamic Matrix A\n",
    "    # see \"Calculate the Jacobian of the Dynamic Matrix with respect to the state vector\"\n",
    "    a13 = float((x[3]/x[4]) * (np.cos(x[4]*dt+x[2]) - np.cos(x[2])))\n",
    "    a14 = float((1.0/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
    "    a15 = float((dt*x[3]/x[4])*np.cos(x[4]*dt+x[2]) - (x[3]/x[4]**2)*(np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
    "    a23 = float((x[3]/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
    "    a24 = float((1.0/x[4]) * (-np.cos(x[4]*dt+x[2]) + np.cos(x[2])))\n",
    "    a25 = float((dt*x[3]/x[4])*np.sin(x[4]*dt+x[2]) - (x[3]/x[4]**2)*(-np.cos(x[4]*dt+x[2]) + np.cos(x[2])))\n",
    "    JA = np.matrix([[1.0, 0.0, a13, a14, a15],\n",
    "                    [0.0, 1.0, a23, a24, a25],\n",
    "                    [0.0, 0.0, 1.0, 0.0, dt],\n",
    "                    [0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "                    [0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "    \n",
    "    \n",
    "    # Project the error covariance ahead\n",
    "    P = JA*P*JA.T + Q\n",
    "    \n",
    "    # Measurement Update (Correction)\n",
    "    # ===============================\n",
    "    # Measurement Function\n",
    "    hx = np.matrix([[float(x[0])],\n",
    "                    [float(x[1])],\n",
    "                    [float(x[3])],\n",
    "                    [float(x[4])]])\n",
    "\n",
    "    if GPS[filterstep]: # with 10Hz, every 5th step\n",
    "        JH = np.matrix([[1.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 1.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "    else: # every other step\n",
    "        JH = np.matrix([[0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "                        [0.0, 0.0, 0.0, 0.0, 1.0]])        \n",
    "    \n",
    "    S = JH*P*JH.T + R\n",
    "    K = (P*JH.T) * np.linalg.inv(S)\n",
    "\n",
    "    # Update the estimate via\n",
    "    Z = measurements[:,filterstep].reshape(JH.shape[0],1)\n",
    "    y = Z - (hx)                         # Innovation or Residual\n",
    "    x = x + (K*y)\n",
    "\n",
    "    # Update the error covariance\n",
    "    P = (I - (K*JH))*P\n",
    "\n",
    "\n",
    "    \n",
    "    # Save states for Plotting\n",
    "    savestates(x, Z, P, K)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Lets take a look at the filter performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plotP():\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.semilogy(range(m),Px, label='$x$')\n",
    "    plt.step(range(m),Py, label='$y$')\n",
    "    plt.step(range(m),Pdx, label='$\\psi$')\n",
    "    plt.step(range(m),Pdy, label='$v$')\n",
    "    plt.step(range(m),Pddx, label='$\\dot \\psi$')\n",
    "\n",
    "    plt.xlabel('Filter Step')\n",
    "    plt.ylabel('')\n",
    "    plt.title('Uncertainty (Elements from Matrix $P$)')\n",
    "    plt.legend(loc='best',prop={'size':22})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Uncertainties in $P$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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SJDMbYWZnSlotaVeUxwQAAAAANFOXLl105JFHqri4WEuWLKm1/uGHH9aCBQt09tln6+KL\nL/ahwtrSormzc+4dMxtQo/lESeudcxslycyelHSepA6S2ssLswfNbJ5zrrzmPs1ssqTJktS/f/9o\nygMAAACA6l6eJu1Y4XcVTXPoSOmcmTHd5ZgxY7Ry5UotXLhQp556amV7bm6urr32WmVmZmr27Nkx\nPWY04nGOax9JW8OWt0nq45y70Tn3C0mPS7ovUmiVJOfcvc650c650d27d49DeQAA+IvZhAEAfhs7\ndqwk6YMPPqjWfv311ysnJ0c33HCDBg8e7EdpEUXV49oczrkHE31MAAAAAJAU857LlmrMmDGSpIUL\nF1a2vffee3rggQc0bNgwTZ061a/SIopHj+sXkvqFLfcNtQEAAAAAAqBPnz4aOHCgdu7cqY0bN6qk\npERXXnmlnHP629/+poyMDL9LrCYePa4fSRpqZgPlBdZLJH03DscBAAAAADTT2LFjtWnTJn3wwQfa\nunWrVq1apUsvvVTjxo3zu7Raor0czhOSFkoaZmbbzOxy51yppCmSXpW0RtLTzrlV0ZcKAAAAAIiV\niuHCjz/+uG699VYdcsghmjVrls9VRRbtrMKT6mifJ2lec/drZtmSsocMGdLcXQAAAAAA6lERXF9+\n+WVJ0qxZs9SjRw8/S6pTPM5xjZpzbq5zbnJWVpbfpQAAAABAUjr88MPVs2dPSdJJJ52kyZMn+1xR\n3QIZXAEAAAAA8bVv3z5JUmpqqu655x6lpAQ3Hga3MgAAAABA3Nx6663auXOnrr76ah177LF+l1Mv\ngisAAAAAtDJvvvmmZs2apUGDBunWW2/1u5wGxeNyOAAAAACAgFm1apXuvPNO7dixQ6+++qrS09P1\n1FNPqX379n6X1iB6XAEAAACgFXj11Vd1//3365133tGYMWP0+uuva/To0X6X1Sj0uAIAAABAK3DN\nNdfommuu8buMZglkj6uZZZvZvXl5eX6XAgAAAADwWSCDK9dxBQAkM+d3AQAAtDCBDK4AAAAAAFQg\nuAIAAAAAAo3gCgAAAAAINIIrAAAAACDQCK4AAAAAgEAjuAIAAAAAAo3gCgAAAAAINIIrAAAAACDQ\nAhlczSzbzO7Ny8vzuxQAAAAAgM8CGVydc3Odc5OzsrL8LgUAAAAA4LNABlcAAAAAACoQXAEAAAAA\ngUZwBQAAAAAEGsEVAIBEc34XAABAy0JwBQAAAIBWZt68eTIzTZw4sbLtnXfeqbNt7NixfpRZieAK\nAAAAAK3M0qVLJUmjR4+ubFuyZEmttkjb+YHgCgAAAACtTKRAWtF2/PHH17udH9J8PToAAAAAJNDt\ni2/Xp7mf+l1GkxzR5QhNPXFqTPdZX49reHCN1AvrB3pcAQAAAKAV2bVrl7Zt26ZevXqpd+/ekqT8\n/HytW7dOPXv2VN++fSVJBQUFWrt2rbKysjR06FA/S6bHFQAAAEDrEeuey5YoUi/qsmXL5Jyr1tu6\nfPlyOec0atQomVnC6wxHjysAAAAAtCLLli2TJI0aNaqyLdIw4cWLF0uSTjjhhARWFxnBFQAAAABa\nkXXr1kmSBg4cWNkWaWKmOXPmSJJOP/30BFYXGcEVAAAAAFqRkpISSdJXX31V2VZz+PBrr72mhQsX\nqm/fvho/fnzii6yB4AoAAAAArcjJJ58sSbrjjju0YMEC7d27Vxs2bFDPnj3VtWtXPfLII7r44ouV\nkpKi2bNnKz093eeKmZwJAAAAAFqVK664QnPmzNHbb7+tcePGqWPHjnLOac+ePerUqZNKSko0ePBg\nPfzww8rOzva7XEkEVwAAAABoVdq0aaM333xTzz//vJ577jnNnz9fBQUF6t27tyZMmKDx48fr/PPP\nV1pacOJicCoJY2bZkrKHDBnidykAAMSck/O7BABAK5eSkqILL7xQF154oS666CI988wzuvvuuwPT\nw1pTIM9xdc7Ndc5NzsrK8rsUAAAAAEhqka7rGjSBDK4AAAAAgPjLzc3Vpk2b1Lt3b/Xq1cvvcupE\ncAUAAACAVqol9LZKAT3HFQAAAAAQf2eddZacC/7cC/S4AgAAAAACjeAKAAAAAAg0gisAAAAAINAI\nrgAAAACAQCO4AgAAAAACjeAKAAAAAAg0gisAAAAAINAIrgAAAACAQCO4AgAAAAACLWHB1cyGm9k9\nZvasmf0kUccFACBonN8FAADQwkQVXM3sATPbZWYra7RPMLPPzGy9mU2TJOfcGufclZIuknRKNMcF\nAAAAALQe0fa4PihpQniDmaVKmi3pHEkjJE0ysxGhdd+U9JKkeVEeNxDKysr8LgEAAAAAkl5UwdU5\n946k3BrNJ0pa75zb6JwrlvSkpPNC27/onDtH0qXRHDcI7p97l4599Fhd+kS236UAAAAAQFJLi8M+\n+0jaGra8TdJJZnaapG9JaqN6elzNbLKkyZLUv3//OJQXG4d1PkTKlTYUbfO7FAAAAABIagmbnMk5\n95Zz7mrn3BXOudn1bHevc260c2509+7dE1Vek5189Dc15sBB7bdS7di/w+9yAAAAACBpxSO4fiGp\nX9hy31Bb0jmhsFCStLtwt8+VAAAAAEDyikdw/UjSUDMbaGYZki6R9GIcjuO7gcWlfpcAAAAAAE3y\n7LPPysw0duzYOrfZvHmzMjMz1blzZ+3e7X9HXbSXw3lC0kJJw8xsm5ld7pwrlTRF0quS1kh62jm3\nKvpSAQAAAADROuaYYyRJq1bVHdOmTp2qoqIi3XzzzeratWuiSqtTVJMzOecm1dE+T0lyyZu6WNjt\ndXvW6ciuR/pWCwAAAAA01uDBg9W+fXvl5uZq+/bt6t27d7X1Cxcu1NNPP63DDz9cU6ZM8anK6uIx\nq3DUzCxbUvaQIUP8LqVe/UtLJEmf5Hyi84ec73M1AAAAABqy47bbVLTmU7/LaJI2w4/QoTfcELP9\npaSkaOTIkVq0aJFWrlxZLbg65/TLX/5SknTHHXcoPT09ZseNRsJmFW4K59xc59zkrKwsv0up16CS\nUnVUG7/LAAAAAIAmqRguvGLFimrtTzzxhD788EOdccYZys7O9qO0iALZ49qSpMhU7sr9LgMAAABA\nI8Sy57IlqwiuK1eurGwrLCzU9OnTlZqaqjvvvNOv0iIKZI9rS2Chk1xTZCpzZf4WAwAAAABNECm4\nzpo1S1u2bNGPf/xjHXXUUX6VFhE9rlGixxUA0FTO+V0BAKC1GzlypMxMq1evVnl5uXJycjRz5kxl\nZWXp1ltv9bu8WuhxjZJJWr17td9lAAAAAECjdezYUYMGDdKBAwe0ceNG3XTTTSooKNCvf/1rdevW\nze/yaiG4RqlAxVq/d73fZQAAAABAk1QMF3788cf1wAMPaMiQIbrqqqt8riqyQAZXM8s2s3vz8vL8\nLqVBp+gwpRkjrgEAAAC0LBXB9ZZbblF5ebnuuOMOZWRk+FxVZIEMri3hcjgmb3amDKUpdBMAAAAA\nWoyK4FpWVqZx48bpvPPO87miutFVGCVjciYAAAAALdB5550n10JmDAxkj2tLUjGrcEv5hQMAAABA\nS0NwjVJK6IKu9LoCAAAAQHwQXJsplFcrT2/deWCnb7UAAAAAQDIjuEbpELWVJH3y1Sc+VwIAAAAA\nyYngGqVB6iJJnOMKAAAAAHFCcI1SSmiwcJkr87kSAEBLw0eeAAA0DsE1ShXnuDI5EwAAAADERyCD\nq5llm9m9eXl5fpfSIKvocS2nxxUA0DiOvlYAAJokkMHVOTfXOTc5KyvL71IaVDFUeE/RHp8rAQC0\nNNbwJgAAQAENri1JptIkSQu2LPC5EgAAAABITml+F9DStbMMdcvspg4ZHfwuBQAAAACSEj2u0XJS\n7/a9mZwJAAAAAOKE4NpMFnZiUoqlEFwBAAAAIE4IrjGQYilyjhkiAQAAACAeCK4xYGYqc1wOBwAA\nAADigeAaA6mWylBhAECTMVYHAIDGIbg2k4Vdfc/MtHzXch+rAQAAAIDozJgxQ2amGTNm+F1KLQTX\nGMgvypeTU15Rnt+lAAAAAEDSIbjGwAVDL5AklZaX+lwJAAAAADTPlClTtGbNGk2ZMsXvUmpJ87uA\nZJBqqZIkx9lKAAAAAFqobt26qVu3bn6XERE9rlFy8s5xlcQETQAAAAAQBwTXZrKquZmUEnoYCa4A\ngEZhgA4AAE1CcI2BFPMeRud4JwIAaDxreBMAAOJi3rx5MjNNnDixsu2dd96ps23s2LF+lFmJ4BoD\nlUOFRY8rAAAAgOBbunSpJGn06NGVbUuWLKnVFmk7PxBco+WqelwZKgwAaArG6QAA/BIpkFa0HX/8\n8fVu54dAzipsZtmSsocMGeJ3KXWyare9JYYKAwAAAMH27tNr9dXWfX6X0STd+nXQmIsOj+k+6+tx\nDQ+ukXph/RDIHlfn3Fzn3OSsrCy/S2mUiqHCpY7ruAIAAAAItl27dmnbtm3q1auXevfuLUnKz8/X\nunXr1LNnT/Xt21eSVFBQoLVr1yorK0tDhw71s+Rg9ri2NG1S20iSFmxZoEEjB/lcDQAAAIC6xLrn\nsiWK1Iu6bNkyOeeq9bYuX75czjmNGjWqsrPOL4HscW1pTu51sqSqc10BAAAAIKiWLVsmSRo1alRl\nW6RhwosXL5YknXDCCQmsLjKSVpScpFRL9bsMAAAAAGiUdevWSZIGDhxY2RZpYqY5c+ZIkk4//fQE\nVhcZwbWZ/O4qBwAAAIDmKCkpkSR99dVXlW01hw+/9tprWrhwofr27avx48cnvsgaCK4AAAAA0Iqc\nfLJ3quMdd9yhBQsWaO/evdqwYYN69uyprl276pFHHtHFF1+slJQUzZ49W+np6T5XzORMAAAAANCq\nXHHFFZozZ47efvttjRs3Th07dpRzTnv27FGnTp1UUlKiwYMH6+GHH1Z2drbf5UoiuEaNS7cCAAAA\naEnatGmjN998U88//7yee+45zZ8/XwUFBerdu7cmTJig8ePH6/zzz1daWnDiYnAqaWE4wxUAAABA\nS5WSkqILL7xQF154oS666CI988wzuvvuuwPTw1oT57gCAAAAQCsW6bquQUNwBQAAAIBWKjc3V5s2\nbVLv3r3Vq1cvv8upE8EVAAAAAFqpltDbKnGOawxUzc60p3CPj3UAAAAAQNOcddZZci1gxll6XJvJ\nwmZnSkvx8v8LG17wqRoAAAAASF4J63E1s/MlnSupk6T7nXOvJerY8ZaRmqGhnYeqrLzM71IAAAAA\nIOlE1eNqZg+Y2S4zW1mjfYKZfWZm681smiQ55/7tnPuxpCslXRzNcYNoQKcBMi6SAwAAAAAxF+1Q\n4QclTQhvMLNUSbMlnSNphKRJZjYibJObQuuTQvBHgwMAAABAyxZVcHXOvSMpt0bziZLWO+c2OueK\nJT0p6Tzz3C7pZefcsrr2aWaTzWyJmS3JycmJpry4MqN3FQAAAAASIR6TM/WRtDVseVuo7SpJZ0j6\ntpldWdednXP3OudGO+dGd+/ePQ7lAQAAAABakoRNzuScu1vS3Yk6HgAAAIDWyznHKEkfxOvSOvHo\ncf1CUr+w5b6hNgAAAACIu9TUVJWUlPhdRqtUXFystLTY94/GI7h+JGmomQ00swxJl0h6MQ7HAQAA\nAIBaOnbsqPz8fL/LaHWcc9q9e7eysrJivu9oL4fzhKSFkoaZ2TYzu9w5VyppiqRXJa2R9LRzblX0\npQIAkBziNIoKABDSpUsX7dmzR1999ZWKi4vjNnwVXlgtKytTQUGBtm3bpqKiInXp0iXmx4mqD9c5\nN6mO9nmS5jV3v2aWLSl7yJAhzd0FAAAAgFaqTZs26t+/v3Jzc7V582aVlZX5XVJSS0lJUdu2bdW+\nfXt17txZKSmxH9ibsMmZmsI5N1fS3NGjR//Y71oAAAAAtDxt2rRRr1691KtXL79LQQzE4xzXVmtD\n3gYVFBf4XQYAAAAAJBWCa7RCw+W7ZHrjuD/P/9zHYgAAAAAg+RBcY2Rs37F+lwAAAAAASYngCgAA\nAAAINIIrAAAAACDQAhlczSzbzO7Ny8vzu5QGcUUoAAAAAIivQAZX59xc59zkrKwsv0sBAAAAAPgs\nkMEVAAAAAIAKBFcAAAAAQKARXAEAAAAAgUZwBQAAAAAEGsEVAIAEc8xJDwBAkxBcY+zjnI/9LgEA\nAAAAkgqBtUKtAAAgAElEQVTBNUYGHzJYkrQpb5PPlQAAAABAciG4RqliuFefDn3UuU1nn6sBAAAA\ngORDcAUAAAAABFogg6uZZZvZvXl5eX6XAgAAAADwWSCDq3NurnNuclZWlt+lNGjR+hy/SwAAAACA\npBbI4NqSTE9/wu8SAAAAACCpEVybK7WN3xUAAAAAQKtAcG2utAytzDxem1L6+10JAAAAACQ1gmsU\nSlLbycn8LgMAAAAAkhrBNRpkVgAAAACIO4JrFGrm1jJXptLyUl9qAQAAAIBkRXCNSvXoWlJeoufW\nPedTLQAAAACQnAiu0XKu8uYRXY5QmqX5WAwAoCVwDW8CAADCEFyjUHOo8DHdj1F6arovtQAAWp5B\n+sLvEgAAaBEIrgAAAACAQCO4RsOk4jIGfAEAAABAPBFco7B970FJ0pLNuT5XAgAAAADJi+AaA298\nusvvEgAAAAAgaRFcY+Dvb23wuwQAAAAASFoEVwAAAABAoBFco9DD9uqIlK3KUInfpQAAAABA0gpk\ncDWzbDO7Ny8vz+9S6nV8yjpJ0qkpKyrbDpYe9KscAAAAAEhKgQyuzrm5zrnJWVlZfpfSKHtdB0lS\naXmpJGnRl4v8LAcAAAAAkkogg2tLUZTWUZJUrhRp52qd3e90SdLeor1+lgUAAAAASYXgGoUlo/8o\nSTrUcqW/f00dlz3mc0UAAAAAkHwIrlEodSZJOsT2eQ3/fVSSdLC4zK+SAAAAACDpEFyjUFruBddr\n056u1n7dM5/omSVb/SgJAAAAAJIOwTUKJeXe926WX2vddc9+kuBqAAAAACA5EVyjMLBbB79LAAAA\nAICkR3CNwrBe9V+up7zcJagSAAAAAEheBNdoWP0P339WfJmgQgAALZbjQ04AABpCcI1GA8F1z/7i\nBBUCAGixNr/rdwUAAAQewTUa6W0jNqd1+EyS9JsXVyWyGgBAS3Rwr98VAAAQeATXaBx6dLXFXqXe\n9VstrcCPagAAAAAgKRFco2EmFzZcuJ1z6lrYXpL5VxMAAAAAJJmEBVczG2Rm95vZs4k6ZkJYarXF\nXpbrUyEAAAAAkJyiCq5m9oCZ7TKzlTXaJ5jZZ2a23symSZJzbqNz7vJojhdIDUzQNGfZtgQVAgAA\nAADJKdoe1wclTQhvMLNUSbMlnSNphKRJZjYiyuMElqWk1rv+2aUEVwAAAACIRlTB1Tn3jqSaY2NP\nlLQ+1MNaLOlJSedFc5xAi9DjOrh7h8rbH2zYnchqAAAAACDpxOMc1z6StoYtb5PUx8y6mtk9ko4z\ns+l13dnMJpvZEjNbkpOTE4fyYqy0qFZTn0Myqy07Li4PAAjDywIAAE2TlqgDOed2S7qyEdvdK+le\nSRo9enTwX9rLS2o1paRUn1V441f7q/XCAgAAAAAaLx49rl9I6he23DfU1mo98N4mv0sAAATVJ0/5\nXQEAAIEXj+D6kaShZjbQzDIkXSLpxTgcJ5CcpNKyEt16/lGVbY99uMW/ggAAwVZe6ncFAAAEXrSX\nw3lC0kJJw8xsm5ld7pwrlTRF0quS1kh62jm3KvpSg+2gy5Aklci0aMeHOm1Yls8VAQAAAEByiOoc\nV+fcpDra50ma19z9mlm2pOwhQ4Y0dxcJt7vtYepbuE7Di4u1tk2G2mWWVVu/fleBhvTo6FN1AAAA\nANByxWOocNScc3Odc5OzslpOr2XfCddIko4qKq5sy2qbXnn7fs5zBQAAAIBmCWRwbVF6Het9P/a7\ntVbd/z+jK28/sXhrrfUAAAAAgIYl7HI4Seuyf0sFO2q3l5dr9IDuia8HAAAAAJIMPa7RattZ6jHc\nu93n+Kr2/btqbfrKyggBFwDQuq19RXLBv2w5AAB+IrjG0jf/WnV7oXd76oQjKpuufHRpoisCALQE\nB/f4XQEAAIFGcI2l4n1Vtz9+UpJ0+akDq21SVs6n6gAAz+tlo/wuAQCAFoHgGktFBbWaMtKqP8Tv\nrM1JVDUAAAAAkBQCGVzNLNvM7s3Ly/O7lKYZdHr15dIiSdKsi46pbPrBgx8lsiIAAAAAaPECGVxb\n4nVcJUkpVQ9nuUla97ok6dyje1XbrLi0PJFVAQAChpNGAABomkAG15YsPTQz5Lz27aXN70qS2qSl\nVttm2pxPEl4XACB4rCLChj7oBAAAkRFcY+zM7sdKkspM0of3VLbPv+brlbfnLPsi0WUBAALorXLv\nNSPSJdQAAEAVgmuMpU+cFbF9SI8O1ZbnLNuWiHIAAAGW41rYKTEAAPiE4BprWf3qXHXF1wdV3r7m\n6Y8TUQ0AAAAAtHgE11hLqfGQ7t1SeXPq2UdUW/XGmp2JqAgAEHRbP/S7AgAAAo3gGm8f/LXyZkqK\nadKJVT2ylz+0xI+KAAABUaR078aXTNoHAEB9CK7xtvgf1RZ/f/7IastzP96eyGoAAAFSqjRt73ma\nlN7W71IAAAg0gmuCpaSYfnXm4ZXLVz2x3MdqAAB+K7c0yXg5BgCgPoF8pTSzbDO7Ny8vz+9SYqOw\n+s9x1fih1ZbveXtDIqsBAASJc9Ku1VJJod+VAAAQWIEMrs65uc65yVlZLfgyASPOq7q9u3Ywved7\noypvz3z5U5WUlSeiKgBAwHy5P/T/P2eNv4UAABBggQyuyeC9kj1VCy9PrbV+wlG9qi0ff+vr8S4J\nABBA72ae5ncJAAAEHsE1xjJSMiRJu0ryqxq3LY647aLp4ytv5xeWamvugbjWBgAIHpN5N/bt8rcQ\nAAACjOAaY6kpqTrrsLOUaqnVV5SV1tr20KxMffOY3pXLY/6wIN7lAQACwLmq23kpodNi1rzoTzEA\nALQABNd4+tZ9VbfXvhJxk7suObba8tNLtsazIgBAwKxNP0KSSWlcEgcAgLoQXOMpfIKmOZMjbmJm\neunqUyuXr3/2ExWWlMW7MgBAQJSVOymtjbRmrt+lAAAQWATXeEprU3W7ZH+dmx3ZO0tH9elUuXzE\nryP3zgIAkk/ewRKptFDat8PvUgAACCyCa7wddkrV7b11DwN+8WenVlt+Y83OeFUEAAiQT3cUqOSk\nn0np7fwuBQCAwCK4xtsF/6i6/cgFdW6WkmJ6+edjKpcvf2iJikoZMgwAyaxnJ29kTmlxoVRyQPpi\nqc8VAQAQTATXeDukX9Xt3evq3XR4r046YUDnyuVhNzFkGACSWf/OXi9rUd/QqJt6RuYAANCaEVwT\nYdjEqtvbl9e76dNXfK3a8uwF6+NREQAgAFLMu4ZrUdYAr2HVHP+KAQAgwAiucbIxb6NKy0PXbj33\nT1Ur7j2t3vuZmZbcdEbl8h9f/Uwbc/bFoUIAgN9SUrzgWpDZ12soPuBjNQAABBfBNQ4qAutnuZ95\nDZ16V9+guO4ZhiWpW4c2mv3dUZXL4/70NpfIAYAklJHmBddX1+VLPUZI61+Xyst9rgoAgOAhuMbB\ntw//tiSpzIWFzYserrr94lUN7uPco3vpuP6HVC5ziRwASD7H9PX+z5tJSk33Gvfv8q8gAAACiuCa\nKMO/WXV75XOScw3e5fmfnlJtecC0l2JdFQDAR+lp3stwaZmThp7lNa573ceKAAAIJoJrophJw86t\nWn71xkbdbe3vzqm2PGDaSyovbzj0AmhhDu6RtnzofUerUfEi/N76r6Tjvuct7GZSPgAAaiK4JtJF\nD1XdXjRbKm/4vNWMtBSt+u3Z1doG3TBPq7bnxbo6AH5Y8aw0I0u6fYD0wFne9xlZ0qwjpZKDfleH\nOLPQrMKLN+VKHQ71Ghf9zceKAAAIpkAGVzPLNrN78/KSLJylpkuHT6hannddo+7Wvk2aPrrxjGpt\n5979ngZMe0kLPuVcKKDFmn2S9Nzlkdflb5N+f6h096hGfciFlqZq5MyEIw/VYV3bSemZUvseUlmx\nVFLoY20AEqLkoLT5PWnrYqm0yO9qgMALZHB1zs11zk3Oysryu5TYu/ixqttL7m90j0r3jm20+paz\na7X/4MGPNGDaSxow7SVd+PcPlLu/OFaVAoinf54h5Xza8Ha5G6Rbukiv3RT/muCL1BTT57sPyDkn\n9T/Ja9y22N+iAMTPuvneyJrfHyo9eK50/5nS73p4bTOypJy1flcIBFIgg2tSS02Tvj6tavkvoxt9\n13YZado881zddO7wiOuXfr5Ho259XQOmvaS/vbWec2GBoHrpWmnbR1XLP10kzcir+rp+kySrfp8P\n/uK9oVn5XEJLRfwdKPYuobZqe7504hVe4/LH6rlHEigplAp2SkUFjZqsEEgafxwiPXZh/dvMPsH7\nfz/351weCwiT5ncBycypjhfj06dLb8/0budvk/K3177Waz1+NGaQLj91oF5dtVNXPro04jZ/eOUz\n/eEV7zqyk07sr5u/MUJtM1KbVD+AOFgzV/rovqrlaVulzE7Vt2nXRZqx13tT/399q6979ofe14SZ\n0klXhq6jgpbseycfpgWf5ehgSZl0WGg2+U+elL71D38LizXnpHtOlXaurHub7Luk4y6TUvhcHUlo\nRoSRhO27e6cHFEY4PW7pg97XIf2lKUuktDbxrhDNsK+oVLfNW6PHP9xSrf3ckb30m+wR6tEp06fK\nkg/BNQ7SQ9fim7Nujo7pfkzkjX7wsvSv0IzBs4Z7vSxNYGaacNSh2jzzXJWXOy3enKsX/rtdTyze\nUmvbJxZvqdZ+6/lH6duj+hJkgUQr3i899b2q5Ru+lDLa1b19m47e/4a8L6Q7R1Rf98o070uSTr1G\nOvWXtQMwWoSOmd5rxsMLP9cJA7pIbbtIB3OlvVu8N6zJYPWL0tPfb3i7uT/3viSpUx/p0meknkfG\ntzYgEeZcUX35V59JHQ+tvd22pdI/x1Vv27vFG0osSddtkNp3i0+NaJKd+YU66bY36lz/0oov9dKK\nLyV5772/d1L/ygn50DzmAjxEZ/To0W7JkiV+l9FkJeUlGvXIKF10+EX69dd+XfeG4Z+8jfmVNP7m\nmBx/V0GhvnPPQn2++0CT73tMv0N04oDOGtG7k4b36qTB3TsoPTV2n3w751RUWq49B4q1K79IO/IL\ntX3vQX2++4BWb8/Xqu152l9cpvYZqerZKVODunfQacO666wje6pHRz6xQgsX/jc/bYuU2cTz+Heu\nlv7+tdjWVJeeI6WBY6Rex0pZfaW0TKm8VCrZ761PSZcsRUpJ9SaeS2vr9f6WFnpD29IzpdQ2Xlt6\nO+9nTW9LD3HIp4tf0xHzvqNPTn9Qh534DR3z29d03rG9ddclx3nDwl+7STryAuk7D/pdavSe+YG0\nak5s9vW956RB4+iRRcuSv93rpKjwm70N/y8sL5demSotvjfy+vP+Jh13aexqRJPMXrBef3z1s2bd\n9/mf/j8d179zjCtq2cxsqXOuwfMnCa5x8vWnvq4z+p9Rf3AtK5FuDfvU7Np1UoceMa2jsKRMt7/y\nqf71/uaY7tdP447ooRvPHa7B3Tv4U0DF3wxvwNEU798tvR76f3D+PdKxk5q/r7xt0p1J0AuV1V8a\n/QPpiHOlrkNbVRgJD65Hf/0CDZj2kiRp88xzpYN7pdsP8zZszBvcIHv9N9L7f65aPvpi7/kf6Xd9\ncK832/6Kp5t+nMHjpGMvlfqd5PVipaS17McNySX8Q8vm/E2vfkF6+rK61//8Y6nzgGaVhqb7nwcW\n6+21ObXa77rkWJ12eA9lpKXok2179fe3N+itz2pvV1NGaoq+/7XDdHTfLPXslKly55RTUKTd+4q1\ns6BQX+4t1NY9B7Qrv0j7ikrVpX2GhvXsqOG9Oum4/ofo+MM6q32blj2IluDqs0YFV0n6dJ70ZNgb\n2CYOGW6qnfmF+vtbG/TgB5vjepxEWX3L2WqXEec/1gO50h8GNrzd8T+Q/t9VUtfB8a0HLU/JQW/2\nyAqx/DvP3+4NGV79Quz26bcjL5C+dZ/Xk5uk6gqum/5vojeU7I5h0r4d0vfmSEPG+1xtM21bIv0z\nrPYbtksZ7Rt//52rpX//RPryv7GvraYOPaVLHpf6HE/gRWyFh86rl0tdBjV/X7s3SH8ZVff6LoOl\nH8335klAXPz0saWat2JH5fKkE/vr/741st777Coo1JjbF6ioNDETbc381khdfEK/FjUsmeDqs0YH\nV6n6J3HHfFe64O/xK6we5eVOW/cc0Kc7CrR+1z59tDm3UZ8UNVWbtBQN7NZefTu304Cu7dSnc1v1\nymqrgd3aq0/ntspITVFRaZkKCkv1xd6DWrhht+5/b5PyDpZE3N99l43WmSN6xrzOWmGjOa54R+pV\nx3nOaD2i/bQ9UZyTivK9MJy7Udq1xgsNezZLZaVe3W06eb1ZpQe968uaSUX7vL8XM29IcVqmt/7g\nHm+bwr3Nq8dSpJtyvNnYk0zN4HrTv1fo0UVb9OAPTtBpw3pI69+QHv2Wt3EjPugoKCzRlMeXR+wF\nqHDVuCH62elDlJmegPkNSoul33WvWr451xtWHo0DudK7f5IW/jW6/TRGx17SZS9K3Q+P/7GQ3Cr+\n/6ekSzd/FZt9lpd7l1Scd23d25z8U+ms30X/d4dK76zN0WUPVF2q7O3rTtNhXZvwYZyklV/kadJ9\ni1RQWBrr8iJafMP4FjE5FMHVZ00KruVl3nUaK/zwVan/yfErrgVzzumTbXk6b/b71dqvGjdEvzpr\nWOwOtPi+ul8QBozx3qBveqdp+/z5J1Lnw6KvrRVxzqm4rFw78gq1duc+Lf18j5Zt2aPd+4p0ypBu\n+vGYQerXpZ7JjYIgfGKlyW9JvY/zs5rgcM4LxpvflZY/Iu1YUfe2P1ssdY/h33cA1AyuFW+IThnS\nVY/96GTvjektoXOgrnhX6nV0xP0s/TxXF/59YZOPH/eJQsI/rGloErJoOSftz/H+J69/Q/r8fWnv\n57E9Rq9jpPP/Hv1EUc5Jrtz7UCaoH2AhdrYskh4427sdrw8ti/dLcyZLn/6n7m0ue0EadFrsj92K\n7C8q1ZG/ebVyecWMsyon1otW3sESLf08V6u35yunoEjpqSnq3rGNunZoo0M7Zaprhwx1aZ+hTpnp\nSks1FZaUaUdeoTbkeO+LXvrkS23PK6xz/zF/jxwHBFefNSm4SrWHf0S6RAaqWbhhtybdt6hyecrp\nQ3Tt2VH+YYa/WQx3405vspn6lByUVjwrzb3ae2NSlxHnSRc+kJS9SM311b4i3f/eJv39rQ3N3seL\nU07R0X0PiWFVMRL+Bj7OpwIkBee8a9U+d3n19iSbiKRmcN1XVKqjQm+KNs8819vozd9J7/zRux3h\nufOzx5ZVzljZXDOyR+h/T2nEqRBNMe+6qgllLn1OGnpGbPcfD/typDdmSMsfbfx90tt5QzN3rvDO\n0W7fzWsrOSAV7JD2bGpaDSf8yOshS2/btPshuCr+/3ce4J2HGm+FedKjF1a/Tni4tEzpmjUMJW6G\nitM5JOnDG8arZ0B7McvLnf7xzkbd/sqn1dorT0MJKIKrz5ocXCVp6UNe6Klw855WNVlJcxSWlOmI\nX79Sufyn7xyjC4/vW8896rH1I+n+Gm+w6pquvjHKy72epPDfabhz/iCddEXkda1AzQ8eYumXZxyu\nH40Z6P9kBXu3Sn8+yrt94w7ekDZVzZEP426Sxl7nXz0xVDO4SlVvjF7++RgN79Wp+nDbb/9LOsob\nOlxcWq7Db3q52v7OGtFTd11yXL2XOduQs08X/2ORvtpXVGvdqt+eHZu/l/wvpVlHeLfbdZWu3xj9\nPv2Q/6X0ws+kDXVf6iKuDjtVuvTppp0THHCFJWX621sbdPcb6yKuP2N4D10/4Qgd3rNjgiuLk+L9\n0m29vdt+nCKyd4v053rOvbz4UWl4duLqacEeXfS5bvq3d/3pO75zjL7d3PeZCZa7v1jfvW+Rbjx3\nuMYM7d7wHXxEcPXZqU+eqi6ZXfTi+S827Y5/Prr6ECd6aBpUVu40+IZ5lcuLbxzftEvnROplPaS/\n9It6hi42VVmJ9ybok6dqr2tMb26S+O/WvTq/xjDv+pxz1KE6c0RPHdUnS307t1Xb9NTKTwydc3rr\nsxz94ME6PlkO8/QVX9OJA334hJne1ujty5HuGFK1PPqH0jfu9K+eGIkUXP/yxjr96fW1ykhN0drf\nh67z/eE/pJev925P26qVu52+8Zf3KvfTuV26lt98VpOO7ZzTC//drl88VX3So5j0IiTrc37fLumD\nu71LFUWrYnKe3EaG+mvXSx2C/aazPvNWfKmfPrasyfdb9usz1aV9RhwqSpD7xktfhN7D+v23sOFN\n6ZEL6l7/4ze9iclQS0lZuYbeWPVBYeWIGMQUwdVnIx/yPuVa8T9NDD/OSb8NG+54+DnSd5+MYWXJ\nqbzcaVBYeG30P5ZXb6w90ceV70mH1j9DXFS+Wi/9tcYLRLQzDQaYc06/e2mN7n+v7mFzd11yrCaO\n7BXVNYMbE4onHHmo/nbpKKWkJOCT7+ID0m29vNvTv5Da+HT5pmRQWiT9LuxSYWOv83pfW7BIwTV8\nBEllr2uN14SBhY/Kyfs7+cO3j9ZFo/tFVcdd89fpzvlrK5ej6nkND62tYYSBc94pIhntQueuOkkV\nl0trxjmsO1ZK95wSeV2PI6WfvN+izotdv2ufzpj1dlT7yExP0ce/OUtt0lrgBEMVfw9XLQvO1QbK\ny6R//1T6pJ73lT96Q+rbYH5oNcKHCG+8bWJi3j+0QoELrmbWXtLfJBVLess591hD92nJwfWOj+7Q\nY58+puXfX970O9ecrOnEK6SJf4hdcUkq70CJjrnlNUnStWcdrinjhtbeqLzMG374ytTa69LbSTdG\nd75Ykyy4TXr79qrl/31JGnBq4o6fAPNX79SPHo78N/zGr74et2vxlpc7vbZ6h658NPKn/P+56lQd\n1Scr4rqYSdaeJz+FP6bf/Ks06vv+1RKlTz98TUe8XD24StKZs97Wul37JEkvXX2qBnfvoBsee0uz\nNn+rcpuBhY/qvzdPUFa72EwMsmX3AY3944LK5WadC/XKDdKi2d7tFv67CYS6hnles0bq1Dvx9TTR\njBdX1brs3rCeHfXoj05S945tIt7HOaeXV+6I2Dv7g1MG6DfZLeja1Zvflx6c6N0O6v//nM+k2SfW\nv83kt1r1hIIbcvZp/J/eVift1ytHvq7eG+q4xvRp06XTpiW2uCSTkOBqZg9I+oakXc65o8LaJ0i6\nS1KqpH8652aa2fcl7XXOzTWzp5xzFze0/5YcXGctnaXH1zyuJd9rZv01w+vXp0mnT49NcUnsP59s\n15THvQ8LPvvdhOqf0s4+WcpZE/mOfr0ZyN0k3X1s1fL3n5cGj0t8HTFWc2hNhZeuPlVH9o5zYIxg\na+4BjfnDgmptdX64EQvhvWTTtkiZif+Zk1LNESkt+BytiuC6YtyDGjm2KrgWlZZp2E2v1Nr+aymr\n9ETG76saojn/PoIv9h7UKTPflCR9/fDueuiHDbyhDffxU9Lzk0MLJs1o5uWPUFthnjSzf/W2gD/v\nwz98kaSbzh2uH41p2oiiotIynXr7AuUUVD8f++Obz4rZBzZxVfEh2/H/K2Xf5WspjZK7UbpvnHcJ\ns4YMPdt7v+TKpeJ93mR6FXqP8gLckDNa/mV4nNN/bj5b30j9sPH3uSlHSmvBw9t91NjgGu3MPw9K\nmlDjwKmSZks6R9IISZPMbISkvpK2hjYri/K4yS8lVbo+bGjl2zOl//zSv3paiG8cXRU+Z7y4qmrF\nv38WObT+YoX3aahfn2B3Geid41rhkQu8SaJasLwDJbVC68Lp47R55rm+hFZJ6telnTbPPFdLb6qa\nfOuO19Zq0r3xmRxKr95YdZvQGjtm3iQnFZ76nnf5k0QrLZYK8+Oy6zZpqXp/Wu0Pr5anjlTxt/5V\n1fCnYd6b441vhYaoRqfPIW316OUnSZLeXpujNV828ufb8GZYaBWhNdYys7zXqMteqGp76nvSnGBO\n7PfTx5ZWC60bbpvY5NAqeX8HH914hj6ZUf387WNueU2LN+VGXWdchf89nvNH/+poii6DpKmbvefa\n1Q2MFFz3qrT0X9Kyh6qHVknavkx6/CKv42VGlrS6ifO8BMWSB6TfHtK00Cp5k+kV7Wt4OzRb1EOF\nzWyApP9U9Lia2dckzXDOnR1arugm3CZpj3PuP2b2pHPukob2HeQe14I3F2jX7ber3/3/VEbf2rOL\nRd3jWmH/bumPYf/009tLN3zRos5zSbSd+YU66Tbvzez635+jtC8+kh4Ie/H79e7gXYqmZk9SkM6J\naYKCwhKNnPFa5fJtF4zUd0/qX889/HHOXe9We2O+/vfnKC2K82trqfi0/YevSf1Pit1+4SkrlW7t\nWrV84f3SyG/H/7grn5Oe/WH1tqFnSZc+0+Rd1dXjGu7LvINKMVOPjm2qhu7WN7yvY2/pooekvic0\n+zXiknsXatFGLxg0OFfAkn9J//lF1XJQh0Qmi8J8aWbYOc2dB0o//2/d2yfYs0u36dpnvEu+9OvS\nVu9eH7vRQ++uy9H3719cuRzVFQTibcWzVZfzaul/E4V50jt3eBOTReOHr0r9T45NTfFU871YuO8+\nLQ06vXaP6r5d0h01Rm8x0qrJEtXjGkkfVfWsSl5g7SNpjqQLzezvkubWdWczm2xmS8xsSU5OThzK\ni43y/ftV/PnnciUl8T1Q+67S9G1VyyX7vT+qz5t+wfnWomenTB1/mDdL8My5/60eWmfkBS+0St6b\nzF/vrlr+yyjvn2EL4pyrFlqX3HRGIEOr5E188/PxVS80Q258WSu2xegNxldhl3ogtMZHapp3ubAK\nz10u/WtiTHoe63RLt9qhVZLWveZ9UFFez7Wbm6lXVlv17JRZ/XzT7sO8XuevTal9h4Lt0v1neq8R\nM7K8r0/n1d6uHo//qOrN5SMLN0feyDlv3+Gh9Tf0tMZdZifveV/xhnjPJu/3EIBJNvceKK4MrZJi\nGlolaczQ7vr01qoBfr965uN6J/zzVUVoveRxf+v4/+zdd3gU1dfA8e+kQgKEEEINvXeE0DtIF0FB\n6Tt+oXkAACAASURBVGJF7D8VRRGxIEqxoK+ioChFERBUQCnSm/SutFACIQIhlISE1N37/jEk2YSU\nTbK7s5ucz/P4mJnMzpyQZDPnzr3n2EIRP+gxSb93sva/d27qg4mWvu8Jk8o4xc9qljJJWscmPY15\n4k3966rdM/NpwMXK6F9z6dpp+6ZUhogslqaJfHFYk1ClVKxS6jGl1DPZFWZSSs1WSgUrpYIDA123\n/LtNeRdPn9QA/NDrzjSx/FXsK6jmjNIHbSYc6pK209lvrNw99PURKT6upT9xdxGWSevRd3tQuljm\nBTicxcvda7PwybTEst+X2+k0fRMmcz7/sH55Z8Cw6Yj8nUdkz80tffJ6fod+03Ehl1O7rPGuH5gt\nBimfWAevnQHNYg1XxpZa9qRp0HOyfjP1diR0yqTYXIpFQ9OS2A2T9KfV2XBz0/jr5Y4AvL38XxKS\nM6zsOfXX3U8kjOhRWVi5uelPc1o8mbbvvZI5fl/tren761I/tle7kCKe7pz7qE/q9qQ/jvHeyn+z\neYUBLL8PdQtp2xRN02fAvBsFz1vMOjQl6D+rSfHGxZYVU1K697UE5UHV+IXcrP2wdVWENQ2e3wtN\nh6ftm9ka/nrbDsEWbvZIXMMBy/r8QXf2FToJpgRuJ922zcncPfQ3gdbPpt8//379hmR2Z7hyzDbX\nKgBK+nixxu+jtB3P73ONGysPLxhvUdl4enW9j6WTO3oxipgE/Q/21te6ULyICxTPANrWLM2x93um\nbp+/dpsa41ex5VQe/80tR5NdoSCHq3Nz098XmwxL2/d9D9hiwyrslpWMyzXWr1epJfiWhneuw2CL\ncdgVL9ruutZy94Qu49OedkyIgJ4fZn7sto/1Kdbv+unV1bNQu2xxGgfpX/czPx6A2EiYVl1/3cKH\n0g68Z6R+TVd4by1o+n4CvSyq0k8KcOxApykZfnsmdVAktMgwQosM41ypF/QBdTs9WdM0jdApfake\n6AvADztC6fP5NpymtWNKr/aSVYyNw1mUrqW/R/SfmbZvclk4txV2zoRrZ4yLLYUpGSaVTt2M7fQu\ndRLmAzBrZC572w6YCd3eSdv++wv9dyTRRrmAsMsaVw/gFNANPWHdCwxTSuV6WMyZ17hGrfyD/157\njeqrV+Fdrdpdn//y4JfMOjKLTzt/Svcq3W178aR4/WlcQhbFMxoOggdmOeeUWEexWAf2q6k9D076\nM4cXOJnEWPjQomDUy/+Cn5Ou5yGtz9nojtUZ36eewdHkzZJ9Yby+9EjqdtUAHzaN7Zy7tiAbJunJ\nAbj+2iZXk3H9X4/J0DaT6bS5Mfc+CN2mf9x0BAz4KvPj9s+DlXeS1lF/QLUOOZ7amjWuNhF7DRYN\ngzAbFyJ7/Rz4lMr5OGFfp/5KP5jQdDj0/8p+gwkZ15fnxI7rz19dcphlB9KWUjlFj82Uga4n1kOl\nFsbG4mxuhsGMhnfvL1YWnt1l3PuJ5eDk42tpsSCGq7cSqFWmGOte6ZS3c4bthTn3pt/nqFoMLsoh\na1w1TfsZ2AnU0TTtoqZpTyilkoHngbXAcWBJXpJWV9enmj6dxWS2QwFlzyLwZpg+fbj5Y3d//p+l\naaPq2z7RW+sUJkqlK17yStKz/H060sCA8sDLN/2T188awMX9xsWTjQW7zqd+7KpJK8DDwZUImdw7\ndTv02m2qvbkqd1OHU5LWZ+0wXVVkr0gJfbCg2p0bjb/eggPz836+1ePSktZKrbJOWgGaj9JblgHM\nu88u613zzDcAnlib9jTWcipbXrx0WD+XJK3OoXYPeCltwI1DP6Wtcf7pIX0mlq2eRp5cnbukFfT1\nnu/6wY8DbT6d+ZOHm/DhA2m9bquPX8X+89e5HpvI7UQDpk5b/jtL0nq3kpX0Aa+glvqMpM7j9f0x\nV2BaNWMqEFsmrU9tgsqtU1sw/f5cu7yft1KL9Eu/IO13IeFW3s8r8pe4KqWGKqXKK6U8lVJBSqk5\nd/avUkrVVkrVUEpNzuk8Io/cPaDfDP0mYvx/0GzU3cdseD+tLPnqN/R5/AWdxTqF02MuAPDJulNG\nRZN3Xj76+rUU33WFI1k0vzbQ27//A8Ca/+X8lMnZebq7ETqlLz88lnbTUWP8KuumoV23KBRSpq4d\nohNWGbUCqt75WVzxApzIw2yLU2th9zf6x17F4Ym/sj8e0vfZ3jgp99d0BA9vfSrbu1H6DWTNe7M+\nNqAmqukIhia+Re34eVx44ZL+Ov+qDgtXWMm/iv69CcqQLIX8BV+3SUtkf3lMb+WUF1/cAz9bNINo\n8RRnnwunavxCqsYvJOntG2nT1V8/pw/2WDq9Pm1A/dblvMWQiWGtKvPbs21Ttwd+vZNmk9ZRf+Ja\nbsU7+H7n+J26o75SnyVLPqXgyXV6f9vO4/TBtNJ19M8tGXmnhc7ybE9hM5ZJ68A5ULEZP++5kLrL\n1zufsxY9vPTfh0Hfp9//URBMrwnJCZm/TmQr31OF7UHTtH5Av5o1az4VEhKS4/FGyGmq8NmbZ+m/\nvD/TO06nV7VemZzBjrJrl5CiVg99zUGxAvYG+3V7uHJU/3jYEqjdk14ztnLi8i12vtmV8n5FjY0v\nL8zm9IVfen4IbZ4zLh4L83eGMnG5PqHCXgU5jHItJoHmH6wH9GnDm1/rkv0LUv4IthwNfezfuy/J\nZGZbyFU+Xx/C4VxURK5cyofaZYsT5F8Uv6KeVCxZlCoBPlQO8CHA1xsvD4fV7LOvef30dVQAj/4J\nVdtb97qbF2BG2lOcXE35vnEePm+sf/xGmP4UOAsOmyqcT1tOXWXU93toWa0US55uY3Q4IidmE2yZ\nqv+XnfGX9MFRa1je4INeFM3NzbolIuEH4Nss3jsH/wj1+lkXQw4iouN59Ie9HMvQfzi4ij9fDL2H\nCiUd8Ld/ShWIvwmjN0OFe+x/vYJCKTj6C6x8CVLqwgxfBrWyGVjL7/UsC8y1ewm6vw+kLXv644X2\nNKxow3Y2SfH62t7MdHgVur5d6GsFWDtV2CkT1xSuvMbV0MTV0rUz8G1X/c3UGk1HQPVOehGSUtX0\nEXpX8dsYOPyz/rF/VX1KG2n93x4ODmLaoCbGxZdfi4bDiT/0j5s9Avf/n7HxkPYmv+31LlQqZeVN\nkAu5EZvIPZP0aplTBzZicIss2vskJ+qNxyH1ps7WIqLj+Wj1CX47aFytu851AmlXozQVShalnJ83\nVQN8CXDm6tHf94YLf+sfPzQPGgzI/vj4KL2NQYq8rFP+eSicXKVPWR6V9dQ3V0lcAbp+vJmzkbGs\nfqkD9cpnnYwLJ3UzTK8ufflo+v3t/gfd38v6dRkHTev0haF6i5fTETHc+6ne1cCqQcu4m/Bpfb2l\nX0ZuHvDyMSiexY19LpnNiibv/cWthLTpwp8+3IQHm9m5TkRKgi/1DfLu4E+w/E4RUnuso89YP6T7\n+3riCtxOTKb+xLWAHQfic3qwVKoGPDgbKjYvdImsJK525jKJq6WYq7BgAFz5J3/n8SoOFZvp/QRL\n1dCnKZWsovey8iiiV7nU3NL+U0pvJWFK1KdGmJIABZ4+eqsfN/ccL5mjz5vqPe1SWPzhUErR5qON\nXI6O55/3elIsv9M/jLTtU9hw50ajaCkYZ1wfu3/Co7jv/7YDBe9pq6Xjl6Lp/bm+1vHIuz0okVnF\n5JRBk+Ll4dUTNru25VPf3PDxcqdbvbIcOH+D8JtxNovHGgOaVqBHg3K0qR6Av28mPe8c7duuEH5n\nfXjZRjBmW+Y3BJZPSyHvAxCmpLQKlS8cgIAamR72z861NFz7sEskrvtCrzPom510rhPI3MdymM1T\nQCUmm/n7TCRL91/k4IWbRMcn4e/jRVRcElFxSTSq6EfzKv7cU7kkdcoVp0opX4p4uuWuuJsjnNkI\nCzL8vA36ARo+mH5fyDr4yaKQTN9PocUTqZspg5bv9qvPo+3uvgfKklKw8YO0egAZ1eiq9z/1zP8T\n0qu3Enjom78JvZZW0fWrYc1oHORn+4HW0B0wt49+L/S/IzkfL7JmOVvGlq22Pq4DMRbT1B9bA1XS\nZpGMnr+Pv45dYWCzID552M4POSKOw6yO+n1xbtTqCZVbpz1cKlZGv5e2xX20wSRxtTNrE9dpHafR\nu1rvTM5gMLMZjv0OSx8HnPdnIE8yGe38afd53vrtHx5qHsT0h1z4qSvAP7/CUouiXG9fM6SCdMqN\ny89PtaZNjVwW7HAx/7chhE/WnaJj7UDmP57JjXvKSPtrZ/Q2KfkUn2Si7ttrsj3myfbVGN2pOmWK\nF8nzdZRSJCSbuRwVz4Xrt/nvZhxnrsZwKOwmBy7czH9P2ywE+HrRtmZp/H08iU8yUbZEEZpV9qdF\ntVL2GViynK0A0P4V6DZRvyFSCmZ1SP80Kr+/U4cXwW9PowLrEfPENq7eSuDUlRg2n4xg0d4wAJpr\nJ1nm/R6bWsyiS98hOZzQeENn72Ln2WtsfLUT1QOLGR2OQ/z7XxR9v9huyLVrBPoysnUVHm5RCR8v\nO/xObJkOmz6w7tjRm9NNfY2OT6Lxnb7d+Rq0jAxJ63udmef26APk+bTu2BWemp/+XnLG4Kb0b1rB\ndgMLMxrDzfMw8neokcOyEpE9y6m83iX0vsX5+T6d26onw5ZePgZ+FdPtSrmnOTGpF0U8HZgI5vR7\nkBdPboAgG5/TziRxtbOcEtfz0ee577f7aFamGfN6zzMgwnxQCmKvwoVdcHCBXuDBVWQxRcdsVtR8\naxVmBYff6YFfUdfoM5qlK8f0ohspcrNeyQYsE6uC/LQ1hVKKdlM28l9UPMueaUvzKhbT5yxvAG0w\nRWz9sSs8Of/u973PhzTlvsYVcDe43UNKsnstNpGQK7dYefhSupYUtlK7bDGWPdPWdj2BT2+AHx/M\n+bh8jvCbzIrh3+3i6/BB+GsxPJjwLgdU7buOS0lcE4Yuw7uOndZy2VDIlVt0/2wrvRqU45vc9jZ0\nISaz4sVFB/nzyKWcD3agmmWKsWxMW/x8bPi3y2yChYPh9Lqsj8nk92HknN1sC4lkVJsqvNc/k/Ym\neXFqLSx8OPPP2eAmXCnFyiOX+GVfGNtC0ooe/vliexpUsMFaRpkmbFsJt/QiRqA/ZRyex8KUy57U\n18+m6Pg6dH3rrsPCrt+mw7RNgBPc01w9CXtmw97vbHO+R1boSwCdnCSudpZT4qqUovH8xrSr2I5v\n7v3GgAgdRClQZn39SmwExN3QGy0n3YakOP3/HkX0KcFFS4JXMXD3AmXSm9r/dxDObYFz2/R9eWVF\n8ZWl+y8y9pfDBFfxZ+kzbbM91iVYvrEDjD3tsGJbM9afYsb6EJ7uVJ03e7tuC5zcSFnTVadscdb8\nr0PaSH3KDcuYHVAufzdxY385zNL9aUlgcBV/Fo1ujYe7axVMik8ycfDCTXadvcaec9fZefZavs53\n8oNeeHvYYATcbIZVY2HfnLs/1+hhGPhtvk6//FA4Ly06BKQlppGqBMEJ6f8GjO9Tl0crXcZrXh8Y\n+Zs+PdIFPL1gH2v/vcL6VzpSs0xxo8OxqWSTmSGzd7Hv/I1MPz9nVDCd65SxauDIZFZci0kgJCKG\nk5dvERJxC7+iXqw6eokL12/fdXyQf1G83N04G5nJ+s9MbHi1EzVs/dT7+jnY+RWE7dYLJrV/WV/2\nk4FSimpvrgLg9OTetn9vUgo2f5R5camnNupr//LpzyOXeG7hgdTtJ9pX4+376uf9hJf/gW/a6f1I\nx7pgBwNnZfkkstUY6J1DwbGMfnsGDi9M285mUGHEd7vZfjrSMWuh80sp/f761iW9mOB/B/WOE1eP\nZ/86Jx9UkcTVznJKXAGG/TmMEt4lCnbi6kKUUtSfuJa4JBM/PdmKdjXzP6XTcBmLZ4zeAhWa2v2y\nKVNqjr/fi6Jerr+2wlrT1pxg5uYzTOrfgJFtqurFRqLvFEvK5x+FlOrXKQ5P7GHbpytOLtlk5mh4\nFEv2hfHznrC7Pv/BgIaMaF3FdhdUCpLjwd3bJsW0pq89wVebzqRuj2hdmfevPI/bpUPw4LfQOMPT\npAu74PueLpW4ht+Mo92UjbSpHsDPo1sbHY5NxCQk0/3TLVyKir/rc5vGdqZaaV8Dokpz8MINBn79\nN5nN2v/7ja6OqZZrYcPxKzwxbx9B/kXZPs7OP7dZzZKwUdGeZ3/az6qjaWsel45pQ3DVPJw3ZR39\nwwug/v35jktYCN0Oc+88AW048O7WMlk58ScsGqZ/XKMbjPw128NT7mnsMhhjhIjjMKsTmCxa7kji\naj8FoR0OSOLqjE5evkXPGfqif4evY7CnqdUg7rr+cfUuMPyXTEfLbeH8tVg6Td+Mj5c7x953ksJj\nDmI2K1pMXk90fBJ7Hg/Ef8GdKZ6ZrJfJjY7TNqU+iSlRxIMj7/a0RbguzWxWjFt2hF/2p5+G7Iw3\nFpZPWiuWLMqON+7c0Ef/B5/emZHwdmT630kXTFwBxi09wuJ9Ycx9rAWd65QxOpx0lFLEJ5n5LyqO\nq7cSSDKZKeLpTilfL/x9vPD2cCM+ycTJy7eYtvYkh8LurrZf3q8IW17r4pRtof769zKjF+xPt690\nMS92j7/XYUsIUm7wt77WhcoBDlqeEnEcZmYYKOk0DrqMz/epU/6epWhbI4BZI5vnbolCyqwbWxYS\nEmlOr4cfB6ZtP7EOKmVTJM5yNppFh4msXLh2m47TnWSasD1E/wc+AU7fJcSlE9cU8sRV2MPrSw+z\nZN9FapUpxrpXnH/ev9X+fDX9moixIXrFORtLKVS0eHRrWlUv2EWZMvP36UhGfbeDkCKP6Dus+MOY\nnbd+O8pPu/Wm5wOaVmDGEOn/Zykx2UztCavT7fvr5Y7ULuscU1UPXLjBgzP1ljtDW1bmowcbpT8g\npeJ0xv6+Lpq4RsUl0XLyeooX8WDnm93wzOUggsms+HHXed5Z8W+Ox9YqU4yqpX2p5O9DSR9PPNw1\nlILrsYkcDruZ5bTevGhSqSS/PN3GKRPWjI79F02fL7al2/fVsGb0bVzerte1WVGmvLqwG77vkX6f\nDZ6+KqX4Zf9FXl+aVg143csdqWXNe0zkafiyeb7/DogcZOwHXKOr/t6ZkSkZJlncl1jxlPGFnw+y\n8vB/zBrZnJ4NytkgWJEX1iauzv8OLYSNTR3YGHc3jZCIGN5Zns/WQM6k7yfwpsXTqY9rwaYP9b5l\nNmI2Kz5Zd4pi3h6FMmkFaFuzdFrSCvm6WVmyNyw1aX2kTRVJWjPh5eFG6JS+/PBYi9R9PT7byvS1\ntms7lFfXYhJSk9aSPp53J60A932m/3/PbH3k28X5FfVkYr/6RMYk8r87T5mtcSU6nqpv/EmN8aus\nSloBQiJiWHfsCt/vOMen604xbc1Jpq89yZzt52yWtM57vCWhU/qy/Ll2LpG0AtSvUILQKX35eniz\n1H3PLTxAm482YLZTJXCAj1bpv3MT+hpU16ByKz0RaWAxfXhaNfj9OX3qfx5pmsbDwZXYM74bPneW\nvnT/bCvP/XSA67E5tCtZ/Zr+/54f5vn6wgoVm+nf+zs9VzmzUX/SfdFiBsLlf9InrROte49YeVh/\nX+5ezzZ9hIV9yRPXPEp94rrqT7yrV8/0mKF/DMXT3ZP5vec7ODqRk8iYBILv9Md8s3ddnu6Uea/F\n/DKZFaHXYtl//gZh12+TaDITm5BMx1qBdKwdaJ+pymazXnH4aoYb++f3Qela+Tr1wQs3eGDm3wxp\nUYkpAxvn/ILMJMRAyFq9cILl+gtLA76GpsPyHqg9vZtWgbJh8gJ2jO+dp7Woh8JuMuCrHQDcW68s\n341yrdL1RkhINlFnQvo2QTYr3JRLSSYztd5KexKc7ROoO+1xKBEEr9xJ2lz0iSvoT6ju/XQLZ67G\n8mK3WrzS/e6qySniEk3Um5h5a6einu40r+KPr7c7SSbF5ah4jl2KznU8fRuVZ2DzijSvXIoSRT2c\nr3eqHSmleOibnekS+YNvd7dLD+WUacJnPuxjeHVzoi7CZw3S73t6G5RrpCex+Vi3/sayI6ltq1Js\nH9eFIP9Mpkan/D3Ia99nkXvXz8EXOdTysLKl2Y3YRO6ZtI6SPp4cmtgjx+OF/chUYTu7sXgJl995\nhyoL5uPTokWmxzy44kFCboSwe9hufDwd16pEWMdyutXwVpWZ/EAmT0tyIfxmHJ+vP8WSfblvDfLj\nE61oX8vGxaJCd8Dy5+DGubR9XsVh3Lk8r39NKSB0V+Ggqyfhq2zWnOTVW5dt0ojeZr5sAZF61cjd\nfVYz+NcbtKpWikWjW+fqZvmf8Cju+z+9P2Rxbw+OvidrWnNj0h/HmLM97ed6wRMt6VDLMRW1U6Tc\nxAOc+6hPzt///wuGayHQdQJ0fM2lE1dIu+EDsmyLkrFKNsCa/3WgbrkSDomxMPnvZhxtp2xM3V7/\nSidqlrFd5eH9568z8Oud1C5bjL9edqIlNvt+gD/+l/nnBv+o/2555b7AVmhkLI/+sIfQa+mrQC97\npg3Nq9yZmnxxH3zXDUrVgBcPZHIWYVfr3oEdM9Lvc/PQ6wlY+ff4jyP/8fzCg/zwWAu6ONma/cJG\nElc7i9m+g7Ann6TKwoX4NMt8et9Huz9i4YmFrB+0nrK+MgXBGW09dZVHvt+Tum1twabEZDNL9oUx\n4XfbTjV+tnMNxvaog5utR7MzloUHKOIHLxwAX+sS5pQnTN4ebpz8oDckJ8IHNkgWqrSD1s9Aycr6\nzfzq19N/flwoFPXP9KUOtfoN2P21/vF9n0Hw46nrU1/tXpsXuln3NHtf6HUGfbMzdbtAFoNwgHOR\nsXT5eHO6ffMeb0mn2vZPYC2T1mPv98THK+eRfW5f16c1gt46KTHGpRNXgFNXbtHjs62p2xP61qN5\nFX9eXXL4rtYuhyZ2p6SP7Z8CijQms6LG+FWp2xtf7UR1G7XNGTJ7J7vOXmfnm10p7+dEg4mg96P9\nrIHeHiQr3SZCm+dzXaBGKcVLiw6x4nDaNP92NQP48YlWaJ/UgZgrORcLEvYVG6m3h/ELynVxrFpv\nrSLJpJyy6F9hI4mrncXs2EHYE09S5acf8WmeeV+xZaeW8e7Od1k3aB3lfGXBt7OyrDQM+vS1Da92\nStdmIDYhmfk7zzN1Tc7r6kr5evF6zzr0blg+xymkRy9G0e/L7Xftf7FrTV7pUScXX4UV4qNgSuXM\nP/fM31C2Qeafu2PRngu88etRlvZIJHjro5kfVKMbdBwLgXX1fr3ceX9x9057ymvNH5aM08DGndf7\nABtl/1xYeWdtTYMH4KG5gN7Cpdfn2zgdEWNVYYffDl7k5cX6mlhPd42QyX3sGHTh8MEfx/jO4ukr\n2PcJbIOJa4hN1HtO57qy6pFf4Ncn9Y9H/g4LBrh04gr6k6nOGQYQLP0ypg0t8tJiROTZ0Nm7Unsn\n759wLwHF8ldNNCouiSbv/UXpYt7sm3CvLUK0L6Vg9zewbiKYslij2msKNByUq97nc3ec492VxwBo\nVsGbX6/fqXTr5G1GRObik0zUfXsNfkU9OfyOTBM2miSudhb7999cePwJqvy4AJ/gzP+dfwv5jYl/\nT2TNwDVULJb3VhnC/hKTzbSdspHImCzWXGbB38eTzwY3pX3N0vkerdseEsmIObvT7ZsxuCkD7rHD\nz05SHMzvrzebz0yLp6DCPaDMeh+1I4uyPtfAOdBokO1jNCXBJIunwTbq3Zdrx/+AxcP1j0tUhFeO\npft0ZEwCHaZuIi7JxJQHGzGk5d2DA0opBny1g8MX9RucFlX9+WVMW7uHXliYzIoJvx+9q/+rLVte\npdzkpPjjhfY0rOiXzSuysGQUHPs9bdvFE1fQf77/OHKJF34+CEC10r7MfawFVQKM7YFamD2/8AB/\nHNGfQJ76oHe+Ck+lTPl21IwGmzKb4cJO+H0M3LyQ+TEPzIImQ6w63e3EZFp9uIFppun0dt+LajoM\nbcDXNgxYOMrXm88wdc0Jp2ztVRhJ4mpnsTt3cuGxx7Nd47rizAre2v4Wqx5YRaUSlRwcociL24nJ\nPDJnT5YVK4e2rMzrPevYpfBFit1nrzF49q50+3a92Y1yfkVsfzGzCVaPg73f5u51NbrBkIXgaYeY\nLGUsbZ+fKVlmE2huuZtKtH8erHwxbTuLkfWUolUApYt5s+GVTqlP2y2fsgK83qsOz3aumfv4RY6U\nUnyx4TSfrT+Vuu+5Lvr0+7wW7DGbFWN+3M9fx66k7lvxfDsaB+VxBoBSem/XlGmNI36Fmt3ydi4h\nsvHoD3vYfPIqLauWYsmYNnk6h1KKam/q04+tWsvtCk79Bds+znzg9pEVULU9uGU94GVKSsR9sp7A\nT262jbfuz2OhQmGoh775m72hN2w6wCnyThJXO4vdtZsLjz5K5fnz8G2Z+Y30H2f/4M1tb7JywEqq\n+lV1bIDC5a06eolnf0or+GD3yrNKweUjsOkjOJW+b+b5Mt14KawTbz45nFY1bFxEKicZk1eAV09B\n8QzrxpPi9fgPzIeDC6w799DFULvn3clsUjxMznD+HKaDZdZbMaNtr3ehUikp1GZvGZ+OAswc3ow+\njazvc3n+Wiydpm++a/9dhcnywnJ9uL1mLIhCz2xWtJ+6kf+i4vM8YLZkXxivLz3CJw81YWDzIDtE\naaDkRP1v3ZJH7v5c5/HQeVzmr5tSGeKjuOBRlY4xH/JG77qMsaIzgVKKE5dvsT0kklvxSQT5+9Cm\nRgBB/kULxoCAC0npSTy0ZSU+elAGHpyBJK52Frt7DxdGjaLy3Ln4tm6V6TELjy/koz0f8UWXL+hS\nuUumxwiRHbNZMXrBftYfT3vak+t1dfmklKLmW6upGuDDhlc7O+y6d5k/AM5ucvx1fQPhtdNWHZpk\nMjNyzm52nb2ebv83I5rRq6H1SZOwDcvqzSlKF/Pm12faZvo7dPN2Ik/M28f+TGZczBkVTDdb9vlL\njIVDC6HZI7kuGCOEtaLjk2j63l+YFSwe3TrX/bfbfLSBS1Hx1hchc2V7voVVY+/eH/wE9Jys1f7j\nGQAAIABJREFUV7hfPBKOrwAg7o0I+s3cxemIGJ7uWJ03ete9KwFVSjFl9QlmbT1rVQiTH2jIg/cE\nUdRLngDa04Kdoby9/F+ZJuxEXDpx1TStH9CvZs2aT4WEhBgdTqZi9+zhwiOjqDz3B3xbt870mH8i\n/2Hon0N5pskzPNv0WQdHKAqSiOh4Wn64IXX7+S41GdvTxsWbspBy8/9k+2pMuK++Q66ZpSv/wtdW\nrg3t9g40HgzFy6fvr2c2Q+g2+OmhrPvIpnhiPVTKfCmAcB2/7AvjtaVHcv06DzeNXeO7UTqfxW2E\nMNL5a3oBLaVg7f86Uqdccate9+eRSzy38IBde507pUuHYVbH7I+5bwYEP0ZMQjK9P99K2PU4ABpW\nLMHg4EpsPnmVDSci8h1KkyA/3uhdj+Cq/nhK1VubqfrGn5Qp7s3u8d3kabeTcOnENYUzP3G9vXcv\n50c+QuUfvse3TeZrRxJMCQT/GMxLzV7iyUZPOjhCURB9u/Usk1cdB6BsCW/W/q+j3VtMDPt2F3+f\nueZ87Sws37vy84dHKYiJ0At4JN2GSq0goBDdpBUikTEJPDJnD8cuRWd73M9PtaZNjdw9mRLCmaX0\nYfVw01gypg3NKmffYux2YjL1J64F8l/cyaVdOgzz+ulV+VP0+wKaj0rdTEg2MeK73ewNzbw2BsDy\n59rRpFLm6+KVUkTGJPLFhhAW7DpvVVjVS/sysk0VOtcpQyX/ok7dykUpRUKymfgkE77eHni6u3Ep\nKo6f94Rx4lI0EbcSqB7oS60yxQm7cZvaZYrxSJuqtm8LeEfIlVt0/2wrg4MrMXWQTBN2FpK42tnt\n/fs5P3wElb+fg2/bzJ8ASeIq7OHqrQS6f7aFm7eTAJg2sDEPt7BP8a+btxNp+v46mlUuya/PtrPL\nNYQwilKKZLPCXdPsdpMkhLPYdCKCx+buBWBS/waMbFM1y2MHz9rJ7nPX7VfZvgC6FBXHm78e5e8z\n12hWuSRv9q6XZbKak8RkM3+fieS9lcc4l6Encl6ULeFNrTLFqVbalyD/onf+70NgcW+KF/HA28PN\nJk8elVKsOnqZ5xYeyPngHJQprg/O27oY5qjv97Dl1FX2vNWNMsXtXGBSWM3axLWAL1iwozu/4Mrs\nvIm/KJgCi3tzaGIPPl57ki83neb1ZUeYs/0cPz3VyuZTGmes16fqv9+/oU3PK4Qz0DQNT3dJWEXh\n0KVuGb57JJgn5+/j7eX/MmN9CHMfa0mjoPRtnfp8vo1jl6JpVa2UJK25UN6vKHMfy2PV+wy8PNzo\nXKfMXesvb95OZNfZa/y0+wLbQiKtPt+V6ASuRCew/bT1rwHw9nCjX5MKdKhVmnrlS1C2RBF8vdxx\nd9NQCq7FJjLv71C+3GRdHYgUQ1tW4uHgSgT4enP9diInLkXj4e6Gt4dbalutiFsJ3DNpHQAPBwcx\nsV8Dini45evpckxCMltOXaV6oK8krS5Knrjm0e0DBzk/bBiVvv2WYh3aZ3qMPHEV9nb2agyDZ+/i\n6i19reb4PnV5qkN1m4ycXotJoPkH66ka4MPm16S4mBBCFAThN+MY8NWO1L8bWTn5QS+8PaRIkKsx\nmxWxiclciornXGQsoZGxnI6I4fTVGC5cu8212ES7x/BE+2q82K0WfkXzVoE9PsnE43P38veZa1ke\n4+Gm8XCLSrSuHkD10r7ULFMsx7Y2b/12lJ92X+CXMW1oUdWAvvAiSzJV2M7iDh0idMhQKn07m2Id\nOmR6TEri2rp8a77tkcs+mULkwuytZ/hw1QlAHyGd0LdettPArDH8u13sOH2N355tyz05rIcSQgjh\nWpYfCuelRYfu2q9pcPx96W1ZmN2KT+Lf/6LZdCKCP45cIvxmXJbHenu4MeG++jwcHGSXgY7TETEM\nmb2LyJgciineMbRlZd7v3+CuYlYXrt2m4/RNBPh6sW/CvVKUyclI4mpncYcPEzp4CJVmfUOxTp0y\nPcZkNtF0QVMqFqvImoFrMj1GCFuJjk9i5qYz/LDjHAnJZmoE+vLZ4KY0Dsr9Gpu/z0Qy7NvddK9f\nlm8fsWPvWCGEEIYymRWh12Jx0zSqBvjIDb1wetdjE1lxKJylBy7yT/jdxfb8fTz5v6HNaF9L7ztv\n2ds7N5W1hePIGld7S1njmk3i7+7mTq+qvThx/YSjohKFWIkinrzRuy5je9Rm8qrj/LAjlPu/3EHp\nYt70aFCWV7vXJsCKNbAR0fEM+3Y3AFMebGTvsIUQQhjI3U2jRmAxo8MQwmqlfL14tF01Hm1XLd1+\npRTzd55n8qrjjJizm5ZVSxEVl8TJK7cAvSiZJK2uzXnrZzu7O4mrKTJ3C92FsDcPdzfe6deAba93\n4fF21Sjm7c7C3Rdo/sF6nv1pPztOR5JkMmf62mP/Raf2i/3koSZWJbpCCCGEEEbTNI1RbauyY1xX\nejUox57Q66lJ6/NdauZ7CZUwnjxxzSO3IneqkcmUGuGkKpXyYWK/+kzsV59tIVf5dN0pVh29zKqj\nlwHw9XInuGopGlX047+bcfx6MDz1te/0q8/A5kFGhS6EEEIIkSeBxb35ZmRzwm/GsfroJe5vWkGq\nCBcQkrjmkVsxfVqNMmf+5EoIZ9KhViAdagVyLjKWv/69TEhEDP+ER7Hl1FW2nLqa7tiZw5vRp1F5\ngyIVQgghhMi/iiWL8mSH6kaHIWxIEte8crtTOS2HPq4KRWh0KFEJUfh5+2V7rBD2Vq20L093qpG6\nnZBsYvXRyxy4cIOude/uGSeEEEIIIYQzkMQ1jzS3O1OEzaZsjwssGghAaHQoTQKb2DssIXLF28Od\nAfdUlCbzQgghhBDCqUlxprxy15+4qiyK3KRoV7GdI6IRQgghhBBCiAJLEtc80tzu/NPJGlchhBBC\nCCGEsCtJXPPqTuKaGBZmcCBCCCGEEEIIUbBJ4ppHbr6++v+9vaw6PjJO+r0KIYQQQgghRF44ZeKq\naVo/TdNmR0VFGR1KljR3d9x8fFDJ2Rdn8i/iD8DGCxsdEZYQQgghhBBCFDhOmbgqpVYqpUb7+Tl5\n+xh3d0wxt7I9pEFAA7zdvfF293ZQUEIIIYQQQghRsDhl4uoyTCYSz57L8bBinsUcEIwQQgghhBBC\nFEySuOaDu78/puvXjQ5DCCGEEEIIIQo0SVzzwc3Hh8TQ0ByPMykT4THh9g9ICCGEEEIIIQogD6MD\ncGVFmzUjISSEkE6d0byyri486VYkiq2cntbDgdE5iKYZHYExCu2XXUi/cCjEP+uF9OuGwvu1F9qv\n2+gAjKMV1u954f6mGx2BMQrh1+1duzYVp08zOgybkMQ1H8q8+gqapyem6OyrH8dEKMJvhVO7RlMH\nReYgyugADKIK6RdeWL9uKMRfe2H9ukEV1u95If2yC+/vOIX3ay+sXzdQWH/RC+v7ukeZQKNDsBlJ\nXPPBvUQJyk14K8fjftk/g/nH5vP0yIIx2iGEEEIIIYQQjiRrXIUQQgghhBBCODVJXB0kyZxEginB\n6DCEEEIIIYQQwuVI4uoAKUUPtl3cZnAkQgghhBBCCOF6JHF1gH41+gGQaEo0OBIhhBBCCCGEcD2S\nuDpAoW4hIoQQQgghhBD5JImrEEIIIYQQQginJomrA62/sN7oEIQQQgghhBDC5TgscdU0rbqmaXM0\nTVvqqGs6iwrFKgAQkxhjcCRCCCGEEEII4XqsSlw1Tfte07QITdP+ybC/l6ZpJzVNO61p2hvZnUMp\ndVYp9UR+gnVV3u7eNA5snFpdWAghhBBCCCGE9TysPG4u8CUwP2WHpmnuwFdAd+AisFfTtBWAO/BR\nhtc/rpSKyHe0QgghhBBCCCEKHasSV6XUVk3TqmbY3RI4rZQ6C6Bp2iKgv1LqI+C+vAakadpoYDRA\n5cqV83oa56Pg+LXjRkchhBBCCCGEEC4nP2tcKwJhFtsX7+zLlKZpAZqmfQPco2nam1kdp5SarZQK\nVkoFBwYG5iM853I9/jo3Em4QlRBldChCCCGEEEII4VIcVpxJKXVNKTVGKVXjzlPZQmVI3SEAJJoS\nDY5ECCGEEEIIIVxLfhLXcKCSxXbQnX0iE0U9ihodghBCCCGEEEK4pPwkrnuBWpqmVdM0zQsYAqyw\nTVhCCCGEEEIIIYTO2nY4PwM7gTqapl3UNO0JpVQy8DywFjgOLFFK/Wu/UF2bu+YOwNrQtQZHIoQQ\nQgghhBCuxarEVSk1VClVXinlqZQKUkrNubN/lVKq9p11q5NtFZSmaf00TZsdFVVwChl1rdwVgHhT\nvMGRCCGEEEIIIYRrcVhxptxQSq1USo328/MzOhSb8fX0NToEIYQQQgghhHBJTpm4FmQms8noEIQQ\nQgghhBDCpUji6iAaGgDf//O9wZEIIYQQQgghhGvxMDqAwsLT3ZNSRUrJlGEhhBBCCCGEyCV54upA\nrcq3wk2Tf3IhhBBCCCGEyA3JohwsMi7S6BCEEEIIIYQQwqU4ZeJaENvhAMQlxRGbFMvZm2eNDkUI\nIYQQQgghXIZTJq4FsR0OQPeq3QGITow2OBIhhBBCCCGEcB1OmbgWVKWLlDY6BCGEEEIIIYRwOZK4\nGiA8JtzoEIQQQgghhBDCZUji6kClffQnrjvCdxgciRBCCCGEEEK4DklcHai2f22KexXHy93L6FCE\nEEIIIYQQwmVI4upgRdyLGB2CEEIIIYQQQrgUSVwdLMmcxLKQZUaHIYQQQgghhBAuQxJXByvqUdTo\nEIQQQgghhBDCpUji6mB9q/fFw83D6DCEEEIIIYQQwmVI4mqAZHMyiaZEo8MQQgghhBBCCJfglImr\npmn9NE2bHRUVZXQoNmdWZgC2XtxqcCRCCCGEEEII4RqcMnFVSq1USo328/MzOhSb61+zPwAJpgSD\nIxFCCCGEEEII1+CUiWtB5ib/5EIIIYQQQgiRK5JFOZibpv+TLz652OBIhBBCCCGEEMI1SOLqYEHF\ngwDwcvcyOBIhhBBCCCGEcA2SuDqYm+ZG08CmaGhGhyKEEEIIIYQQLkESVwMoFLsu7cJkNhkdihBC\nCCGEEEI4PUlcDZCyzjUyLtLgSIQQQgghhBDC+UniaoD7a9xvdAhCCCGEEEII4TIkcTVQeEy40SEI\nIYQQQgghhNOTxNUAlYpXAmD35d0GRyKEEEIIIYQQzk8SVwM0K9sMAHfN3eBIhBBCCCGEEML5SeJq\noF2XdhkdghBCCCGEEEI4PUlcDZDypPVc1DmDIxFCCCGEEEII5yeJqwHcNDd6V+uNj4eP0aEIIYQQ\nQgghhNOTxNUgGhoXbl0g0ZRodChCCCGEEEII4dQkcTWIQgFw7NoxgyMRQgghhBBCCOcmiatBHqj5\nAABmZTY4EiGEEEIIIYRwbk6ZuGqa1k/TtNlRUVFGh2J3ey7vMToEIYQQQgghhHBqTpm4KqVWKqVG\n+/n5GR2K3VT3qw5AeEy4wZEIIYQQQgghhHNzysS1MCjrW5YyPmVw0+RbIIQQQgghhBDZkazJQLeT\nbvNryK9GhyGEEEIIIYQQTk0SVwMFFA0wOgQhhBBCCCGEcHqSuBqoR5UeAJjMJoMjEUIIIYQQQgjn\nJYmrgVJa4Wy5uMXgSIQQQgghhBDCeUniaqD7a9wPwM2EmwZHIoQQQgghhBDOSxJXA5XwLgHAmnNr\nDI5ECCGEEEIIIZyXJK4G8vPS+9RKL1chhBBCCCGEyJqH0QEUZp7unjQObCzFmYQQQgghhBAiG/LE\n1WAxiTH8e+1fbiXeMjoUIYQQQgghhHBKkrgarG2FtgDEJsUaHIkQQgghhBBCOCdJXA1Wy78WAMev\nHTc4EiGEEEIIIYRwTg5LXDVNG6Bp2reapi3WNK2Ho67r7Or41wHgxPUTBkcihBBCCCGEEM7JqsRV\n07TvNU2L0DTtnwz7e2madlLTtNOapr2R3TmUUr8rpZ4CxgCD8x5ywVK3VF0AQqNDjQ1ECCGEEEII\nIZyUtU9c5wK9LHdomuYOfAX0BuoDQzVNq69pWiNN0/7I8F8Zi5dOuPM6l5YYn0x0ZBwmkzlf59E0\nDYB159fZIiwhhBBCCCGEKHCsSlyVUluB6xl2twROK6XOKqUSgUVAf6XUUaXUfRn+i9B0U4HVSqkD\ntv0yHC/0SCQLJuzkVmR8vs7jprkRXDYYP28/G0UmhBBCCCGEEAVLfta4VgTCLLYv3tmXlReAe4FB\nmqaNyeogTdNGa5q2T9O0fVevXs1HeK6jhFcJIuMiCYsOy/lgIYQQQgghhChkHFacSSn1hVKquVJq\njFLqm2yOm62UClZKBQcGBjoqPEMFlwsGICIuwuBIhBBCCCGEEML55CdxDQcqWWwH3dkncimlJc5f\noX8ZHIkQQgghhBBCOJ/8JK57gVqaplXTNM0LGAKssE1YhUu9UvUAuJ182+BIhBBCCCGEEML5WNsO\n52dgJ1BH07SLmqY9oZRKBp4H1gLHgSVKqX/tF2rB5eftRxH3Ivx++nejQxFCCCGEEEIIp+NhzUFK\nqaFZ7F8FrLJpRICmaf2AfjVr1rT1qZ1WsjnZ6BCEEEIIIYQQwik5rDhTbiilViqlRvv5FZ4WMY83\nehyAiNtSoEkIIYQQQgghLDll4loY+Xv7A7Dr0i6DIxFCCCGEEEII5yKJq5PoVKkTAOvPrzc4EiGE\nEEIIIYRwLpK4OomAIgGATBUWQgghhBBCiIwkcXUSPp4+1C1Vl3+v/SuFmoQQQgghhBDCgiSuTkRD\nA+Dq7asGRyKEEEIIIYQQzkMSVycypO4QALaFbzM4EiGEEEIIIYRwHk6ZuGqa1k/TtNlRUVFGh+JQ\nLcu1BOBS7CWDIxFCCCGEEEII5+GUiWth7OMKUKFYBQC+O/qdwZEIIYQQQgghhPNwysS1sHLT3Cji\nXgQAszIbHI0QQgghhBBCOAdJXPNIKf3/ifG2rQDcolwLAI5cPWLT8wohhBBCCCGEq5LENY+UWc9c\nTcnKpudNKdC08sxKm55XiPy4EX+DrRe3siVsC5djLxsdjhBCCCGEKGQ8jA7AVfn4eekfKNsmrg0C\nGgCw+eJm3uZtm55bCGvFJccxftt41l9Yn+1xE1pNYHDdwQ6KSgghhBBCFFaSuOZRSs9V26atEFA0\nAICI2xE2PrMQOTt94zTfHPmGtaFrrTr+g90f8MHuD5jbay7Nyza3c3RCCCGE87iVeIslJ5ew9/Je\nqpeszrC6wwgqHmR0WAK9VkzIjRA2hW3i2LVjJJmTqB9Qn85BnakbUBdPN0+jQxR5IIlrXqVMsrZ1\n5go0K9OMAxEHuBB9gcolKtv+AkJkcOzaMb4+9DWbL25O3fdSs5d4tMGjeLjd/TahlGLFmRVM2DEB\ngEfXPEr9gPosvm+xo0IWQgghHC7sVhh9fu1z1/4d/+1gwbEFAAyrO4w3Wr6BpmmODq9Q+/3077y9\nI+vZitvDtzP7yOzU7XvK3MOcnnMkiXUhssY1j1LeipSNpwoD9K3eF4CfT/xs83MLYel89Hle2fwK\ng/8YzM5LOxlZfyTrBq3j6KijPNnoyUyTVgBN0+hfsz9HRx2le5XugJ78NprXiERToiO/BCGEEMLu\nTl4/ybit4+5KWsv4lKFjUMd0+xaeWEjj+Y2JS45zZIiFUlRCFDMPzaTRvEaZJq3lfMvRqnwrgssG\nU8yzWLrPHYw4SLMFzaSujAvR7JF42UpwcLDat2+f0WFk6uLJGyz/7CADXr6HinX8bXruW4m3aPtz\nWwCOjjpq03MLAXAz/iYzD89k8cnFuGluDK4zmNGNR1OqSKk8ne/k9ZMMWjkodXv7kO34eReuPsxC\nCCEKnou3LjJ1z1Q2X9yMm+ZGt8rdGFRrEG0qtMn0ieq2i9t4dsOzqdvy99A+wmPC+eGfH/g15FeS\nzEkAFPcszrc9vqVB6QY5vv7szbP0X94/dbtluZbM6TnHbvGK7Gmatl8pFZzjcc6YuGqa1g/oV7Nm\nzadCQkKMDidT4adu8PunB+n/8j0E2ThxBWg0rxEAe4bvoahHUZufXxReK8+sZPre6dxIuEGfan14\nsdmLVCxWMd/nvRZ3jc5LOqdurxm4xibnFUIIIRwtMi6SLw9+ybKQZQDU8a/DzHtnUsanTI6vvZ10\nm1YLW6Vu7x+xHy93L7vFWpicuXmGWUdmsfrcagA6BnXk8YaP57nOxvS905l/bD6gP51dN2idzWIV\n1rM2cXXKqcJKqZVKqdF+fs47QpUyyGavxL9hQEMADkUcssv5ReETFh3G0+ueZvz28fh5+7Gg9wKm\ndpxqs+QyoGgA+0akzZDotawXJ6+ftMm5hRBCCEe4nXSbrw99Te9lvVkWsoze1XqzcsBKlt6/1Kqk\nFcDH04e9w/embjf/UYoX5teJ6yd4aeNLDFg+gDXn1tCvej+WD1jOV92+yldxyNdavMaUDlMAuBx7\nmde3vG6rkIUdOGXi6hpSMlf7nP3pJk8DpI4CCZFXSeYkZh6ayf3L72fP5T28cM8L/Nr/V5qWaWrz\na3m7e3Ng5IHU7UErB7H70m6bX0cIIYSwJbMyM//f+XRf2p2Zh2dSP6A+i+5bxLSO06jqVzXX5yvi\nUYSND21M3f6/g/9nw2gLj7DoMN7a/hYPrXyIjWEbGVR7EGsGruHDDh9S3a+6Ta7Rt3rf1OR1dehq\nqzsrCMeTxDWPUpc12Clx7VypM6BXQBMir45dO8aDyx/k68Nf07xsc5b3X87oxqPtWkHP082Tw48c\nTt1+8q8npfCBEEIIp7UjfAcPLH+A6fumU8anDF91+4p5vefRICDntZLZCfQJZEaXGQDMPjKb89Hn\nbRFuobAlbAuN5zWmz299WHFmBd2rdGfVA6t4p807VChWwebX61u9L/1r6Gtex24Zy834mza/hsg/\naYeTV3cyV0esET5z8ww1Staw+3VEwaGU4qtDX/Hd0e/wdvfmw/Yf0q9GP4dd301z4+ioo7T4sQXx\npnjGbx/PxZiLPNPkGYfFIIQQQmQnMi6SGftnsPzMcgDeaPkGw+oOs2kbm26Vu1Hbvzanbpzivt/u\n4/Ajh3HT5LlRZhJNiby38z1WnFmRuq9V+Va81eotqvlVs/v1P2j/QerPQofFHTjyyBFpaeRk5Dcn\njzT7zhQGSL3J//zA53a8iihojl07Rv/l/Zl1ZBa+nr782v9XhyatlvaO2EvNkjUBmHloJi9tfMmQ\nOIRwJbeTbnM++jzhMeGp1TKFcLQDVw7Qa1kvGs1rRKN5jWgyvwlrzq1xyIC9vZnMJj7e+zFdlnRh\n+Znl3Fv5XrYP2c7wesPtkqgsum9R6sef7vvU5ucvCPZc2kPzH5unJq3lfcuzfMByvuvxnUOS1hSW\na5Mn757ssOsK6zhlVeEUztwO5/K5KJZN3c99zzehSsMAu1wjMi6SLku6AMioj7DK/H/nM33fdAAe\nrPUg77Z51yl+bl7f8jqrQ1enbsuIs3BWSeYktoRt4cfjP3Ly+klKFy1Nl8pdGFBzgM3WU2VkVmYm\n75rMklNLsj1u9YOrCSoeZJcYhAB9hteA5QNyPC6oWBArBqzA091+y07s5XLsZR5d8yjhMeEAvNPm\nHQbVHpTDq/Jv68WtPLfhOf3jwVvxL2L7jhSuyPJeF6Brpa5M7zTd0CrMli2NNj60kUCfQMNiKSxc\nuh1OCmdOXK+ci2bp1H30fa4xVRuVttt1UtriLO23lDql6tjtOsK1XY69zITtE9h9eTclvUsys9tM\nGgU2MjqsdL498i1fHPwidbsgtHpKMiUxfd90fj7xc6afn9NjDi3Lt3RwVCK34pPjeeqvpzh01boq\n7iPqjeDV4FfxcMv7ahuT2cS28G3subyHBccW5Oq1ciMlbC00KpRP9n3C5oub0+3vUaUHzcs2x9vd\nmxkHZnAzIf26v4ltJvJQ7YccGGn+LDi2gOl7p6NQ9KnWh8ntJ+fr9zi32v3cjujEaACOjjrqsOs6\nq5VnVjJ++/jU7S2Dt+S5n7yttfypJXHJcYB8rxxBElc7uxIazdIp++j6SD3qtS1vt+vM+3ceH+/7\nmErFK7HqwVV2u45wXX+e/ZMJOyaQbE6mXql6/NT3J7sWX8qPjI3Zf+n3C3VL1TUworzZEraF5zc+\nb/Xxmx7eROmi9hvgEnmTZEri68Nf8+3Rb+/6XMViFQkoEsDVuKtcir2U5Tm+6vYVHYM6WnW9+OR4\nJv49MbX/oKWyPmWZ33t+pkVHTl4/yaCV6Z8I9a7Wm6kdpjrFjArhuiLjIvlk3yf8cfYPACr4VuDV\n4FfpUbVHlq/ZEb6DMevHpNt3aOQh3N3c7RprftxOus3gPwYTGh1KLf9avN/2fRqWbujwOGISY2jz\ncxsAh9eecCZxyXHc9+t9RMRFEFAkgJebv0z/mv2NDisdy16877V9jwdrPWhwRAWbJK52di08hkWT\n9tBlZF3qt7N9dbMUlr84BeEJlbCd6/HXeWfHO2y+uJmyPmV5v+37tK3Y1uiwcvRfzH/0XNYzdfux\nho/xSvNXDIzIOiaziZc2vcSWi1vS7S/uVZzPu3xOcNng1CTicuxlui/tnu646Z2m06tqL4fFK7K3\n6uwqJu+enPr0o5Z/Leb2mksJrxJZviYuOY6pe6ayLGRZpp+vWqIqoxuPpmW5lhTxKMKl2EusOLMi\n2yeqH7T7gPtr3G9VAprZz9Xe4Xsp4lEkx9cKYSnBlMDMQzP5/p/vAegY1JFXg1+1ejq8UopH1zzK\ngYi09mebH95MQFH7LJ3Kj3Xn1/HKZv1vTOPAxsztNdfQwd2UBxJQOO/r4pLjGLNuDAciDtCiXAu+\nufcbQ6cFZ2fxicV8sPsDAA6MPOC0DwUKAklc7ezW9Xjmj/+bLiPqUr+9/RJXgO5Lu3M59rLL3OAL\n+1t1dhWTdk0iJimGIXWGMLbFWLzdvY0Oy2pJpiSa/dgs3b4DIw445XqpszfP0n/53SPBUzpMoW/1\nvtm+NuPanbHBYxnVYJTNYxTWC48J5+0db7P38l6KexXnteDXGFBzQK6fXEbcjqDbL91abZ8BAAAa\nNUlEQVRyff0i7kX4rud3NAlskuvXpvi/g//H7COzU7e/6/Edrcq3yvP5ROGhlGJZyDI+2fcJMUkx\n1CtVj/Gtxue5r/fO/3Yyet3o1G1n+llUSvHMhmfYEb4DgKkdptKneh+Do9KlLAPzcPPg4MiDBkdj\nf9GJ0Sw6sShdL9txLcYxov4IA6OyTsr3qmlgUxb0yd2yDmE9SVztLPZmAnPf2EGnYXVo2LGiXa91\n+sZpHljxAOD803GEfUXGRTJxx0S2hW+jTNEyTOk4hRblWhgdVp69tuU11oSuSd3+tPOndK/SPZtX\nOIZZmZm0axJLTy1Nt7+4V3F+u/83yvqWzdW5msxPS1Lebv02D9d52GaxCusopVh0chHT9kwjWSUz\not4I/tf8fzYZ8AmNCuWLg1+w7vy6TD8/pM4QXmz2IsW9iuf7WinORp2l/+9pAyrjW41naN2hNju/\nKHhmHZ7Fl4e+BPT3sjdbvmmTqao342/SYXGH1O1nmjzDs02fzeYV9nc9/jqdFndK3V714CoqFa9k\nYETphUWH0ec3PYn+suuXdKrUKYdXOLfIuEj2Xt7LmnNr2Bi2McfjneFnxFqhUaH0+13/Pflr4F+U\nL2a/5YGFmSSudnY7OpEfXt9OxyG1adTZ/lUeU0Z8Xmr2Ek82etLu1xPOZ/GJxUzdO5UkcxIDaw3k\njZZvFIgpgkeuHmH4quHp9u0YuiPbKZv2ci7qHPf/fv9d+wfXGcz4VuPzVQm5y5IuRMZFAjCr+yza\nVnD+ad0FRWRcJOO2jmPP5T1ULl6Z6Z2mUz+gvtFh5VuyOZl7FtyTuj24zmAmtJ5gYETCGW0P384z\n69N6aA+oOYB327xr00HwjD+LVUtUZcWAFYaswd5wfgP/2/w/AGqWrMnSfkudcsDfstr+7mG78fH0\nMTgi64RFh/H+rvfZdWlXrl87uM5gxgaPdbl7l06LO3E9/joghZrsRRJXO4uLSeT7sdvpMLgWjbvY\nfxRvbehaxm4ZC0grkcLGsqBRYNFApnWcRnC5HH+3XYrJbKLZj80wK3O6/Y5IYJPMSby9423+PPvn\nXZ9bfN9imyY4KQNQAOsGraOcbzmbnVtkbv359YzfPp645DhG1h/Jy81fLlDrlJRStF/UPnWtbg2/\nGvw+4HeDoxLOwPKpXorf+/9OjZI17HbNp9c9zd///Z267eg12FP2TOGn4z8B8ErzV3is4WMOu3Zu\nKaVoPL9x6raztj2MjIvk5U0vW111vXLxyvSs2pMulbpQp1Qdp12/mhuxSbG0XtgaKBhPyJ2RJK52\nFh+bxJxXt9HmgRo061nF7tezfIPrU60PUztOtfs1hbGiEqJov6h96nbTwKb80OsHh5bud7TMnr6C\nPq3oqcZP2SzhiEuO44sDX/Dj8R/v+lyPKj2Y1nGaXUboTWYTTRekrSVz1nW9BcGtxFuM2zqObeHb\nKOldks86f1bgBnwsjVk3hh3/7UjddtQA57Frxxj8x+BMP/dsk2cZ02SMU96MF2TxyfG0+Cn9EhJH\nFoebfWR2urWMP/b5MV9ruq1l+QTTmdqqZOfq7at0/aUr4DxrKJVSrD2/lte2vJbtcc82fZZhdYfh\n5+3noMiMZTkoIsv2bE8SVztLTjQx68Ut1O9QgS7DHdPOY9/lfTy2Vh89dLb1GsJ2ksxJdFjUgdik\n2NR9X3T5gi6Vu2TzqoJlxZkVvLX9rSw/H1QsiMcaPkaHih0I9AlMl8yblZm45Dgux14m5GYI+y/v\nZ9W5ValPpLLiqJsry0rhINOO7OHLg18y68gsAO6tfC8ftP8AX09fg6Oyvxn7ZzDnnzmp29uHbLfL\nTaVZmXl63dNWTxXsXbU30zpNs3kcIj2lFE+ve5qdl3am7htRbwTjWo5zeCwZByGrlKjCigEr7DKY\nkrEXqKu1H1tzbg2vbdWTRKPWft6Iv8Erm19h35Ws77lndJ5B18pdC+1AlOUDpJ5Ve/Jxp48Njqhg\nkcTVAb4as5Em91ai/aBaDrum5VRDmTJcsNxKvEXbn9Ove2xboS3f3PtNof1DcT76PP1+64fCPu9T\n41qMY3i94Q7/97WcwjekzhDeap11ki6sl7Egi1E37UayXN8HersdW/VHNCszQ/4YwvHrx9PtL120\nNJ90+oSGpRuioXHo6iGeWPvEXb+3S/stpU6pOjaJRaS34NgCpu1NGxwo41OGNQPXGDotPuMgHcD7\nbd/ngVoP2OT8Wy9u5bkNz6Xb56rtoSynWD/a4FFeDX7VrtdTSrE5bDMvbnoxy2M6VOzA1I5TbVpU\nztVZVtHeOngr/kX8DY6o4JDE1QG+fXkrQXX96f10o5wPthHL5KaaXzVWDFjhsGsXdFdir7D63GrW\nhq7l9M3TeLp5Ui+gHj2q9KBblW52GcGNT47ns/2fsfDEwrs+t3PoTop5FbP5NV1VkimJdefX8cn+\nT4i4HZHr17cu35qR9UfSunxrp1hzY9nSxNZraQuj7//5ns/2f5a6vez+ZdT2r21gRP/f3p1HR1nf\nexx/f7OxhH0TDKtgqRiUrUrQcriAChYFb2urvS5VCq3Vi9Aei96e09vltNar51ZsXWldqgWrYLlc\ncaGyKcpFUFygiHBcgLAEkC0LIcl87x/zECcbmWQymUnyeZ0zh3l+88wz3xm+yeT7/H7P75c4O4/t\n5Bt/r7hUUyyTv5SFyrj51ZsrrNkJ8PwVz/PVLjWPOHJ3Zq2axepdq8vbxvcZz7zx8+oVh1S1YucK\nZq+aXaFt5dUr6d62e4IiquqBdx9g/ofzK7TdPuJ2pmdPr/NJw5CHuP+d+3liyxMV2pvDOtk5C3LI\nL8kHIDM9k3XXrmvQk6q7j+9mzuo5fPTFRzXu89uLf8uUs6a02JPl0YjsQNKIqYbTpAtXM7sCuGLQ\noEEztm/fnuhwavTQLSs58yudmTZneO07N6DIYSVzRs7h5uybG/X1m4vCkkJmr5pdYVhVtHq06cHM\n82Yyod8EurTuElXP98myk7x/4H3uWHMHh04cqnG/N77zBp1ad6pzTNL0RH4BbrxuY5NaizdZFJcV\nc9uK28qHrY7rPY4/TPhDLc9q/irP8gqQYim8cc0bUU94Vt0oEKj7xGKHig4x7rlxFdoWfmMh2d2y\noz6GVDT/g/k8sOmBCm0PTniQsb3HJiii06uu9/WU7537Pb4/9Ps1Dmvfk7+Hezfcy2s7X6vy2OwR\ns5k+dHqDxppIE5+fyP7C/eXbvx/3eyb2m1jn47g72w5v42drf8bHhz+ucb8BHQcw/5L5dVriraWL\nvC75/nH3M6Ff3dfzlqqadOF6SrL3uD732w0c2Hmc63+TE9fXqe7M15xVc9hyaAsAt57/I6aePS2u\nMdRXfE/a1f3gZV7KrStuY8fh2k+IuDXez8b07Ol895zvNomznE0hxprEPfQ6Hr+krIQJz3/5pbfm\nO2tO+/laPXI+ak3wv/WuN+7i9dzXAUhPSeOpSU/Rv2P/hn+hOCWOGaRnpBIKxe93zdrctcxaWXU4\nYJu0Ntw37j5G9hhZPgKhuKyYt/a8xU9WVz9MccnUJfTt0De8UY+QZ62cxdo9a8u3e7TtwctXvdxo\nv1PidclB3AVhr9q1utoJc2aPnM1151Sd1C7Rqvu0DxUdYvLi2HtGf3XRr5k0IA49rEmQIg+/9xBP\nbHmySvv8S+cztNvQCifK3Z2jxUdY/tk/uO+d6K65nDvqp0wbdBUpKbrUrF4c5r4+lzW71wDhzoZk\nn2TRUoz0Vsk9mZQK10aw/E+b2b6x7kMWRURERERE4q1H/w5cfWdyz6ofbeHafNfVaAQTbxrCwBE9\nOHmiNG6vcbrzCiEP8Yt1v6jQNvdrc5Nn9sw4nhOJ5oTL5oObWbx9cbWPfa3n17h8wOXVPlb3WCBE\nGcWlJyksLeBk2UncnYzUVrRJa0PrtNakRUybnsTnimoX5+Cb8mcTS+wvffoS7+WF18i7atA0zqly\nvWsT/twb8NgnSouYV2l45OT+kzmv+3k1PCM28T6x++aiHQCMuKwf6a0b52z4waKDLNha9Zr6ykad\nMZKcM8ecfgRADB2lyz5Zxo4jO6q03zDkhpgmPHGHkJdxsuwkxWXFFJUWUVBSQH5JPvkl+ZSGSikq\nLcJxUi2VjJQMWqW1Ij0lnfSUdFItlRRLxcxwD1ESKqG4rJj8knyOFh/lSPERjp08Xv83Xv93Vn7v\npuyb6NSq+V1OUhIq4YsTX1BYUkhGagadWnUiM70tjT4cJIlGnxSVFrFg6wKOFh+tfWdz0lPSmXLW\nFPp3GNA0Ju9Mos+6Lswg93hu+fwkl/WfxHndG2++m7pq2yHx83o0FPW4NnGVF7AGGNptKM9c/kzT\n+KXVwF77/DXmrJ5T7WPZXbN55vJntPaWJKXI610fnfgoY7KqXlvYUq3NXcstr91Spf2DGz5o0kPX\nH/zhSgBufWR8giNJjMprVUv1ZgydwQ/O/4GugRfcnTIvKz/x0hL/zksmkxdPZnf+bqDu1/5LRRoq\n3ML8ffvf+flbP6/S/sjERxhTy1nzpsrdef/A+1z/8vWn3a+prekmLVPIQ5z/ly/Xkf3Nxb/hyoFX\nJjCixDh28hjLP1vOL9f9ssZ9msvPdEsvXE85fvI431z6TfYW7E10KHXWp30frv7K1fTr0I9emb3o\n2qYrmemZZKRklK8v3Ry/f0UkPOP6sKeHlW8nejUId+fQiUMs2bGEee9+OXt7VrssXvnmKwmLKxoq\nXFugklAJFy+8mMLSwkSHknBPXPYEo3om93h+kcpKQiWMeHpE+Xaf9n1YdtWyJvGH76megBOlJygs\nLeRo8VHyCvPIzc9ld/5uPjv6GR8f/pjc/Nx6v0ZzKVhPUeFaVchDrN+7noUfLWTVrlXV7pOZnsnw\nHsMZ1n0Y53Y7lwEdB9C5VWdap7VWD5SINKp9Bfu4ZNEl5dtrvrOGLq27xHzckIfYV7CP1btWs2TH\nkirrZ9dVsi/do8K1BSsuK2bG8hlsytuU6FAaTWZ6JouvXExWu6xEhyISk+qWjbik3yXcM/Ye0lOi\nm7mwLFTG4eLDFJQUcPjEYfIK89hbsJd9Bfs4UHSAg0UHOVh0kC9OfMHxhFyvF72nJz/NsB7Dat+x\nCVLhKiLS9G3Yt4GbX/1yacq7v343U86aEvXz9+bv5cerf8zmQ5sbPLY/jv8jY3uPTfoT4CpcBQif\nsVm3Zx2PfvBonQvZFEuhT/s+9OvQj4EdB9K/Y396Zvaka+uutM9oT0ZqBimWQqqllk9iUt0PRpmX\nEfIQBSUFHCk+wpETR8gryiOvMI89+XvYX7if/QX7yc3PpSRUUmtcF/a8kLkXzGVAxwHlQ7FEmhN3\n5+t/+3p0E3I0caN7jWZ83/Hk9Mqhd/veLepnWoWriEjzsG7POmb+Y2aFtjkj53DjkBsrzK0S8hBv\n73ubGctnxPR67dPbc1738xjeYzgjzhjBoE6D6NSqU9IXqDVR4Soi0sR9cvQTpi6Zmugw6NSqE4M7\nD2Zgp4H07dCXnpk96d6mOx0yOtAuox1t09qSkZpBajAbq0Rn0T0bGTSyB8Mm9k10KCIiEqP9BfuZ\nuGhiTMfI7prN3Avmkt0tu0WdyFXhKiLSTJSFylj26TJ+te5XFJcVV7tPVrsscs7MYXSv0QzpOoQ+\n7fs0cpQiIiKyYOsC7n777lr3y2qXxbx/mcfgLoMbIarkpsJVREREREQkAUpDpWzYt4F1e9YBMKrn\nKEadMYq26W0THFnyibZwbTl90CIiIiIiIo0gLSWNnDNzyDkzJ9GhNBuaN15ERERERESSmgpXERER\nERERSWqNVria2Tlm9oiZLTKzWxrrdUVERERERKRpi6pwNbPHzSzPzDZXap9kZtvMbIeZ3Xm6Y7j7\nVnf/IfBt4KL6hywiIiIiIiItSbQ9rk8CkyIbzCwVeBCYDAwBrjWzIWY21MxerHTrETznSmAZ8FKD\nvQMRERERERFp1qKaVdjdXzez/pWaLwB2uPsnAGb2LDDV3e8GptRwnKXAUjNbBiyobh8zmwnMBOjb\nV4uyi4iIiIiItHSxLIeTBeyK2N4NXFjTzmY2DvhXoBWn6XF198eAxyC8jmsM8YmIiIiIiEgz0Gjr\nuLr7amB1Y72eiIiIiIiINA+xzCqcC/SJ2O4dtImIiIiIiIg0mFgK1w3A2WY2wMwygGuApQ0TloiI\niIiIiEhYtMvhLATWAYPNbLeZTXf3UuA24FVgK/Ccu2+JX6giIiIiIiLSEkU7q/C1NbS/RByWtjGz\nK4ArBg0a1NCHFhERERERkSYmlqHCcePu/+vuMzt27JjoUERERERERCTBkrJwFRERERERETlFhauI\niIiIiIgkNRWuIiIiIiIiktRUuIqIiIiIiEhSU+EqIiIiIiIiSS0pC1czu8LMHjt69GiiQxERERER\nEZEES8rCVcvhiIiIiIiIyCnm7omOoUZmdgD4PNFxnEY34GCig5BmSbkl8aC8knhQXkm8KLckHpRX\nyaefu3evbaekLlyTnZltdPdRiY5Dmh/llsSD8kriQXkl8aLcknhQXjVdSTlUWEREREREROQUFa4i\nIiIiIiKS1FS4xuaxRAcgzZZyS+JBeSXxoLySeFFuSTwor5ooXeMqIiIiIiIiSU09riIiIiIiIpLU\nVLjWk5lNMrNtZrbDzO5MdDyS3Mysj5mtMrN/mtkWM7s9aO9iZv8ws+3Bv50jnnNXkF/bzOyyiPaR\nZvZh8NgDZmaJeE+SPMws1cw2mdmLwbbySmJiZp3MbJGZfWRmW80sR3klDcHM5gTfg5vNbKGZtVZu\nSV2Z2eNmlmdmmyPaGiyPzKyVmf0taF9vZv0b8/1J9VS41oOZpQIPApOBIcC1ZjYksVFJkisFfuLu\nQ4DRwK1BztwJrHD3s4EVwTbBY9cA5wKTgIeCvAN4GJgBnB3cJjXmG5GkdDuwNWJbeSWxmge84u5f\nBc4nnF/KK4mJmWUBs4BR7p4NpBLOHeWW1NWTVP0/b8g8mg4cdvdBwO+Be+L2TiRqKlzr5wJgh7t/\n4u4ngWeBqQmOSZKYu+9193eD+8cJ/xGYRThvngp2ewqYFtyfCjzr7sXu/imwA7jAzHoBHdz9/zx8\ngfpfIp4jLZCZ9Qa+Afwpoll5JfVmZh2BscCfAdz9pLsfQXklDSMNaGNmaUBbYA/KLakjd38d+KJS\nc0PmUeSxFgET1KufeCpc6ycL2BWxvTtoE6lVMNxkOLAeOMPd9wYP7QPOCO7XlGNZwf3K7dJy3Q/8\nFAhFtCmvJBYDgAPAE8EQ9D+ZWSbKK4mRu+cC9wE7gb3AUXdfjnJLGkZD5lH5c9y9FDgKdI1P2BIt\nFa4ijcjM2gGLgdnufizyseBsn6b5lqiZ2RQgz93fqWkf5ZXUQxowAnjY3YcDBQRD7k5RXkl9BNcc\nTiV8cuRMINPMrovcR7klDUF51DypcK2fXKBPxHbvoE2kRmaWTrho/au7vxA07w+GqhD8mxe015Rj\nucH9yu3SMl0EXGlmnxG+ZGG8mT2D8kpisxvY7e7rg+1FhAtZ5ZXEaiLwqbsfcPcS4AVgDMotaRgN\nmUflzwmGtXcEDsUtcomKCtf62QCcbWYDzCyD8AXfSxMckySx4LqIPwNb3f2/Ix5aCtwY3L8R+J+I\n9muCWe0GEJ4w4O1gCMwxMxsdHPOGiOdIC+Pud7l7b3fvT/j30Ep3vw7llcTA3fcBu8xscNA0Afgn\nyiuJ3U5gtJm1DXJiAuE5H5Rb0hAaMo8ij/Utwt+v6sFNsLREB9AUuXupmd0GvEp4RrzH3X1LgsOS\n5HYRcD3woZm9F7T9B/A74Dkzmw58DnwbwN23mNlzhP9YLAVudfey4Hk/IjybXhvg5eAmEkl5JbH6\nd+CvwcnZT4CbCJ/sVl5Jvbn7ejNbBLxLOFc2AY8B7VBuSR2Y2UJgHNDNzHYD/0nDfvf9GXjazHYQ\nngTqmkZ4W1IL08kDERERERERSWYaKiwiIiIiIiJJTYWriIiIiIiIJDUVriIiIiIiIpLUVLiKiIiI\niIhIUlPhKiIiIiIiIklNhauIiEiUzKzMzN6LuPU3s1Fm9kDw+PfM7I/B/WlmNiTG12trZn81sw/N\nbLOZrTWzdmbWycx+1BDvSUREpCnQOq4iIiLRK3L3YZXaPgM2VrPvNOBFwmsHRsXM0ty9NKLpdmC/\nuw8NHh8MlADdCK8/+FD0oYuIiDRd6nEVERGJgZmNM7MXK7WNAa4E7g16ZgcGt1fM7B0ze8PMvhrs\n+6SZPWJm64H/qnT4XkDuqQ133+buxcDvgIHBse8NjnOHmW0wsw/M7JdBW38z+yjotd1qZovMrG3c\nPgwREZE4UY+riIhI9NqY2XvB/U/d/arqdnL3t8xsKfCiuy8CMLMVwA/dfbuZXUi4t3R88JTewBh3\nL6t0qMeB5Wb2LWAF8JS7bwfuBLJP9f6a2aXA2cAFgAFLzWwssBMYDEx39zfN7HHCPbX3xf5RiIiI\nNB4VriIiItGrbqhwrcysHTAGeN7MTjW3itjl+WqKVtz9PTM7C7gUmAhsMLMcoKjSrpcGt03BdjvC\nhexOYJe7vxm0PwPMQoWriIg0MSpcRURE4i8FOHKaoregpie6ez7wAvCCmYWAy4HFlXYz4G53f7RC\no1l/wCsfMvqwRUREkoOucRUREYmP40B7AHc/BnxqZlcDWNj5tR3AzC4ys87B/QxgCPB55LEDrwI3\nBz27mFmWmfUIHusb9NICfBdYG/M7ExERaWQqXEVEROLjWeAOM9tkZgOBfwOmm9n7wBZgahTHGAis\nMbMPCQ8D3ggsdvdDwJvBEjn3uvtyYAGwLth3EV8WttuAW81sK9AZeLgB36OIiEijMHeNGBIREWmO\ngqHCL7p7doJDERERiYl6XEVERERERCSpqcdVREREREREkpp6XEVERERERCSpqXAVERERERGRpKbC\nVURERERERJKaClcRERERERFJaipcRUREREREJKmpcBUREREREZGk9v/Sn482LKNzSQAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a32a8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotP()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cudBjmqAkqUdmGiWWclmmk4DPV9V64PPt7dnuAn6vqg4AngGcmOSAkeXvqqqn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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ace2b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 6))\n",
    "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Covariance Matrix $P$ (after %i Filter Steps)' % (m))\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(6))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,4.5])\n",
    "plt.ylim([4.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Kalman Gains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DGQcFmCg7UOgicNe8PjLsCJKkO7tP0INfTtLkBy7g7C4AAABC0b7b+BZt36nH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\no8KOERlfjF0YdoSUembgDN3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qd8r+OnCXVpz5DcCzA2eEHQHNRKELpJF8Veqjgvt1bE79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\nAAAAANCSBEdOM5WZacyYMXrllVfknJOZ6Z577tF7772nF154QXl5eV5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ze9zM3jWzd8zs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\nNs0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ad1ad90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "plt.step(range(len(measurements[0])),Kx, label='$x$')\n",
    "plt.step(range(len(measurements[0])),Ky, label='$y$')\n",
    "plt.step(range(len(measurements[0])),Kdx, label='$\\psi$')\n",
    "plt.step(range(len(measurements[0])),Kdy, label='$v$')\n",
    "plt.step(range(len(measurements[0])),Kddx, label='$\\dot \\psi$')\n",
    "\n",
    "\n",
    "plt.xlabel('Filter Step')\n",
    "plt.ylabel('')\n",
    "plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n",
    "plt.legend(prop={'size':18})\n",
    "plt.ylim([-0.1,0.1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## State Vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plotx():\n",
    "    fig = plt.figure(figsize=(16,16))\n",
    "\n",
    "    plt.subplot(411)\n",
    "    plt.step(range(len(measurements[0])),x0-mx[0], label='$x$')\n",
    "    plt.step(range(len(measurements[0])),x1-my[0], label='$y$')\n",
    "\n",
    "    plt.title('Extended Kalman Filter State Estimates (State Vector $x$)')\n",
    "    plt.legend(loc='best',prop={'size':22})\n",
    "    plt.ylabel('Position (relative to start) [m]')\n",
    "\n",
    "    plt.subplot(412)\n",
    "    plt.step(range(len(measurements[0])),x2, label='$\\psi$')\n",
    "    plt.step(range(len(measurements[0])),(course/180.0*np.pi+np.pi)%(2.0*np.pi) - np.pi, label='$\\psi$ (from GPS as reference)')\n",
    "    plt.ylabel('Course')\n",
    "    plt.legend(loc='best',prop={'size':16})\n",
    "\n",
    "    plt.subplot(413)\n",
    "    plt.step(range(len(measurements[0])),x3, label='$v$')\n",
    "    plt.step(range(len(measurements[0])),speed/3.6, label='$v$ (from GPS as reference)')\n",
    "    plt.ylabel('Velocity')\n",
    "    plt.ylim([0, 30])\n",
    "    plt.legend(loc='best',prop={'size':16})\n",
    "\n",
    "    plt.subplot(414)\n",
    "    plt.step(range(len(measurements[0])),x4, label='$\\dot \\psi$')\n",
    "    plt.step(range(len(measurements[0])),yawrate/180.0*np.pi, label='$\\dot \\psi$ (from IMU as reference)')\n",
    "    plt.ylabel('Yaw Rate')\n",
    "    plt.ylim([-0.6, 0.6])\n",
    "    plt.legend(loc='best',prop={'size':16})\n",
    "    plt.xlabel('Filter Step')\n",
    "\n",
    "    plt.savefig('Extended-Kalman-Filter-CTRV-State-Estimates.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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REWkD/vbZev7w8TrG9Urg1ZvGKdmVY0ZYSBC/OHMAr944Dufgsmfm85fp66is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9SwnOMrJQX3X9XSVvT5Q6tp5PAnCb4wuvJRpyTjQyQr8X/TDVyvlHRu5yzYwZcw13eu7iUkm4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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b2e9590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotx()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Position x/y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "#%pylab --no-import-all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plotxy():\n",
    "\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "\n",
    "    # EKF State\n",
    "    plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5)\n",
    "    plt.plot(x0,x1, label='EKF Position', c='k', lw=5)\n",
    "\n",
    "    # Measurements\n",
    "    plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements', marker='+')\n",
    "    #cbar=plt.colorbar(ticks=np.arange(20))\n",
    "    #cbar.ax.set_ylabel(u'EPE', rotation=270)\n",
    "    #cbar.ax.set_xlabel(u'm')\n",
    "\n",
    "    # Start/Goal\n",
    "    plt.scatter(x0[0],x1[0], s=60, label='Start', c='g')\n",
    "    plt.scatter(x0[-1],x1[-1], s=60, label='Goal', c='r')\n",
    "\n",
    "    plt.xlabel('X [m]')\n",
    "    plt.ylabel('Y [m]')\n",
    "    plt.title('Position')\n",
    "    plt.legend(loc='best')\n",
    "    plt.axis('equal')\n",
    "    #plt.tight_layout()\n",
    "\n",
    "    #plt.savefig('Extended-Kalman-Filter-CTRV-Position.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WjhGLSLmXkQHDhkFwMEREwMmTmb8GB8Pw4Zed3K5evZoqVaowduzYnLYmTZrw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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b2fc7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotxy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Detailed View"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plotxydetails():\n",
    "    fig = plt.figure(figsize=(12,9))\n",
    "\n",
    "    plt.subplot(221)\n",
    "    # EKF State\n",
    "    #plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5)\n",
    "    plt.plot(x0,x1, label='EKF Position', c='g', lw=5)\n",
    "\n",
    "    # Measurements\n",
    "    plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements', alpha=0.5, marker='+')\n",
    "    #cbar=plt.colorbar(ticks=np.arange(20))\n",
    "    #cbar.ax.set_ylabel(u'EPE', rotation=270)\n",
    "    #cbar.ax.set_xlabel(u'm')\n",
    "\n",
    "    plt.xlabel('X [m]')\n",
    "    plt.xlim(70, 130)\n",
    "    plt.ylabel('Y [m]')\n",
    "    plt.ylim(140, 200)\n",
    "    plt.title('Position')\n",
    "    plt.legend(loc='best')\n",
    "\n",
    "\n",
    "    plt.subplot(222)\n",
    "\n",
    "    # EKF State\n",
    "    #plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5)\n",
    "    plt.plot(x0,x1, label='EKF Position', c='g', lw=5)\n",
    "\n",
    "    # Measurements\n",
    "    plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements', alpha=0.5, marker='+')\n",
    "    #cbar=plt.colorbar(ticks=np.arange(20))\n",
    "    #cbar.ax.set_ylabel(u'EPE', rotation=270)\n",
    "    #cbar.ax.set_xlabel(u'm')\n",
    "\n",
    "    plt.xlabel('X [m]')\n",
    "    plt.xlim(160, 260)\n",
    "    plt.ylabel('Y [m]')\n",
    "    plt.ylim(110, 160)\n",
    "    plt.title('Position')\n",
    "    plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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48GBWr14NwMqVK3nsscey+tLS0pg4cSIBAQE0a9aMTz/9FIDr16/TpUsXWrRoQdOmTfnx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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bf31110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotxydetails()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "As you can see, complicated analytic calculation of the Jacobian Matrices, but it works pretty well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## Write Google Earth KML"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Convert back from Meters to Lat/Lon (WGS84)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "latekf = latitude[0] + np.divide(x1,arc)\n",
    "lonekf = longitude[0]+ np.divide(x0,np.multiply(arc,np.cos(latitude*np.pi/180.0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Create Data for KML Path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Coordinates and timestamps to be used to locate the car model in time and space\n",
    "The value can be expressed as yyyy-mm-ddThh:mm:sszzzzzz, where T is the separator between the date and the time, and the time zone is either Z (for UTC) or zzzzzz, which represents ±hh:mm in relation to UTC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import datetime\n",
    "car={}\n",
    "car['when']=[]\n",
    "car['coord']=[]\n",
    "car['gps']=[]\n",
    "for i in range(len(millis)):\n",
    "    d=datetime.datetime.fromtimestamp(millis[i]/1000.0)\n",
    "    car[\"when\"].append(d.strftime(\"%Y-%m-%dT%H:%M:%SZ\"))\n",
    "    car[\"coord\"].append((lonekf[i], latekf[i], 0))\n",
    "    car[\"gps\"].append((longitude[i], latitude[i], 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from simplekml import Kml, Model, AltitudeMode, Orientation, Scale, Style, Color"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# The model path and scale variables\n",
    "car_dae = r'https://raw.githubusercontent.com/balzer82/Kalman/master/car-model.dae'\n",
    "car_scale = 1.0\n",
    "\n",
    "# Create the KML document\n",
    "kml = Kml(name=d.strftime(\"%Y-%m-%d %H:%M\"), open=1)\n",
    "\n",
    "# Create the model\n",
    "model_car = Model(altitudemode=AltitudeMode.clamptoground,\n",
    "                            orientation=Orientation(heading=75.0),\n",
    "                            scale=Scale(x=car_scale, y=car_scale, z=car_scale))\n",
    "\n",
    "# Create the track\n",
    "trk = kml.newgxtrack(name=\"EKF\", altitudemode=AltitudeMode.clamptoground,\n",
    "                     description=\"State Estimation from Extended Kalman Filter with CTRV Model\")\n",
    "\n",
    "# Attach the model to the track\n",
    "trk.model = model_car\n",
    "trk.model.link.href = car_dae\n",
    "\n",
    "# Add all the information to the track\n",
    "trk.newwhen(car[\"when\"])\n",
    "trk.newgxcoord(car[\"coord\"])\n",
    "\n",
    "# Style of the Track\n",
    "trk.iconstyle.icon.href = \"\"\n",
    "trk.labelstyle.scale = 1\n",
    "trk.linestyle.width = 4\n",
    "trk.linestyle.color = '7fff0000'\n",
    "\n",
    "# Add GPS measurement marker\n",
    "fol = kml.newfolder(name=\"GPS Measurements\")\n",
    "sharedstyle = Style()\n",
    "sharedstyle.iconstyle.icon.href = 'http://maps.google.com/mapfiles/kml/shapes/placemark_circle.png'\n",
    "\n",
    "for m in range(len(latitude)):\n",
    "    if GPS[m]:\n",
    "        pnt = fol.newpoint(coords = [(longitude[m],latitude[m])])\n",
    "        pnt.style = sharedstyle\n",
    "\n",
    "# Saving\n",
    "#kml.save(\"Extended-Kalman-Filter-CTRV.kml\")\n",
    "kml.savekmz(\"Extended-Kalman-Filter-CTRV.kmz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exported KMZ File for Google Earth\n"
     ]
    }
   ],
   "source": [
    "print('Exported KMZ File for Google Earth')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To use this notebook as a presentation type:\n",
    "\n",
    "`jupyter-nbconvert --to slides Extended-Kalman-Filter-CTRV.ipynb --reveal-prefix=reveal.js --post serve` \n",
    "\n",
    "Questions? [@Balzer82](https://twitter.com/balzer82)"
   ]
  }
 ],
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